Solve Using the Square Root Property 100=1.76x^2-13.32x+41

$100 = 1.76 x^{2} - 13.32 x + 41$

Rewrite the equation as $1.76 x^{2} - 13.32 x + 41 = 100$ .

$1.76 x^{2} - 13.32 x + 41 = 100$

Move $100$ to the left side of the equation by subtracting it from both sides.

$1.76 x^{2} - 13.32 x + 41 - 100 = 0$

Subtract $100$ from $41$ .

$1.76 x^{2} - 13.32 x - 59 = 0$

Factor $0.04$ out of $1.76 x^{2} - 13.32 x - 59$ .

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Factor $0.04$ out of $1.76 x^{2}$ .

$0.04 (44 x^{2}) - 13.32 x - 59 = 0$

Factor $0.04$ out of $- 13.32 x$ .

$0.04 (44 x^{2}) + 0.04 (- 333 x) - 59 = 0$

Factor $0.04$ out of $- 59$ .

$0.04 (44 x^{2}) + 0.04 (- 333 x) + 0.04 (- 1475) = 0$

Factor $0.04$ out of $0.04 (44 x^{2}) + 0.04 (- 333 x)$ .

$0.04 (44 x^{2} - 333 x) + 0.04 (- 1475) = 0$

Factor $0.04$ out of $0.04 (44 x^{2} - 333 x) + 0.04 (- 1475)$ .

$0.04 (44 x^{2} - 333 x - 1475) = 0$

Divide each term by $0.04$ and simplify.

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Divide each term in $0.04 (44 x^{2} - 333 x - 1475) = 0$ by $0.04$ .

$\frac{0.04 (44 x^{2} - 333 x - 1475)}{0.04} = \frac{0}{0.04}$

Cancel the common factor of $0.04$ .

$44 x^{2} - 333 x - 1475 = \frac{0}{0.04}$

Divide $0$ by $0.04$ .

$44 x^{2} - 333 x - 1475 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 44$ , $b = - 333$ , and $c = - 1475$ into the quadratic formula and solve for $x$ .

$\frac{333 \pm \sqrt{{(- 333)}^{2} - 4 \cdot (44 \cdot - 1475)}}{2 \cdot 44}$

Simplify.

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Simplify the numerator.

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Raise $- 333$ to the power of $2$ .

$x = \frac{333 \pm \sqrt{110889 - 4 \cdot (44 \cdot - 1475)}}{2 \cdot 44}$

Multiply $44$ by $- 1475$ .

$x = \frac{333 \pm \sqrt{110889 - 4 \cdot - 64900}}{2 \cdot 44}$

Multiply $- 4$ by $- 64900$ .

$x = \frac{333 \pm \sqrt{110889 + 259600}}{2 \cdot 44}$

Add $110889$ and $259600$ .

$x = \frac{333 \pm \sqrt{370489}}{2 \cdot 44}$

Rewrite $370489$ as $7^{2} \cdot 7561$ .

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Factor $49$ out of $370489$ .

$x = \frac{333 \pm \sqrt{49 (7561)}}{2 \cdot 44}$

Rewrite $49$ as $7^{2}$ .

$x = \frac{333 \pm \sqrt{7^{2} \cdot 7561}}{2 \cdot 44}$

Pull terms out from under the radical.

$x = \frac{333 \pm 7 \sqrt{7561}}{2 \cdot 44}$

Multiply $2$ by $44$ .

$x = \frac{333 \pm 7 \sqrt{7561}}{88}$

Simplify the expression to solve for the $+$ portion of the $\pm$ .

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Simplify the numerator.

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Raise $- 333$ to the power of $2$ .

$x = \frac{333 \pm \sqrt{110889 - 4 \cdot (44 \cdot - 1475)}}{2 \cdot 44}$

Multiply $44$ by $- 1475$ .

$x = \frac{333 \pm \sqrt{110889 - 4 \cdot - 64900}}{2 \cdot 44}$

Multiply $- 4$ by $- 64900$ .

$x = \frac{333 \pm \sqrt{110889 + 259600}}{2 \cdot 44}$

Add $110889$ and $259600$ .

$x = \frac{333 \pm \sqrt{370489}}{2 \cdot 44}$

Rewrite $370489$ as $7^{2} \cdot 7561$ .

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Factor $49$ out of $370489$ .

$x = \frac{333 \pm \sqrt{49 (7561)}}{2 \cdot 44}$

Rewrite $49$ as $7^{2}$ .

$x = \frac{333 \pm \sqrt{7^{2} \cdot 7561}}{2 \cdot 44}$

Pull terms out from under the radical.

$x = \frac{333 \pm 7 \sqrt{7561}}{2 \cdot 44}$

Multiply $2$ by $44$ .

$x = \frac{333 \pm 7 \sqrt{7561}}{88}$

Change the $\pm$ to $+$ .

$x = \frac{333 + 7 \sqrt{7561}}{88}$

Simplify the expression to solve for the $-$ portion of the $\pm$ .

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Simplify the numerator.

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Raise $- 333$ to the power of $2$ .

$x = \frac{333 \pm \sqrt{110889 - 4 \cdot (44 \cdot - 1475)}}{2 \cdot 44}$

Multiply $44$ by $- 1475$ .

$x = \frac{333 \pm \sqrt{110889 - 4 \cdot - 64900}}{2 \cdot 44}$

Multiply $- 4$ by $- 64900$ .

$x = \frac{333 \pm \sqrt{110889 + 259600}}{2 \cdot 44}$

Add $110889$ and $259600$ .

$x = \frac{333 \pm \sqrt{370489}}{2 \cdot 44}$

Rewrite $370489$ as $7^{2} \cdot 7561$ .

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Factor $49$ out of $370489$ .

$x = \frac{333 \pm \sqrt{49 (7561)}}{2 \cdot 44}$

Rewrite $49$ as $7^{2}$ .

$x = \frac{333 \pm \sqrt{7^{2} \cdot 7561}}{2 \cdot 44}$

Pull terms out from under the radical.

$x = \frac{333 \pm 7 \sqrt{7561}}{2 \cdot 44}$

Multiply $2$ by $44$ .

$x = \frac{333 \pm 7 \sqrt{7561}}{88}$

Change the $\pm$ to $-$ .

$x = \frac{333 - 7 \sqrt{7561}}{88}$

The final answer is the combination of both solutions.

$x = \frac{333 + 7 \sqrt{7561}}{88}, \frac{333 - 7 \sqrt{7561}}{88}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{333 + 7 \sqrt{7561}}{88}, \frac{333 - 7 \sqrt{7561}}{88}$

Decimal Form:

$x = 10.70088722 \dots, - 3.13270540 \dots$

Solve Using the Square Root Property 100=1.76x^2-13.32x+41

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