Find the Roots (Zeros) y=x^2-7x+7

$y = x^{2} - 7 x + 7$

Set $x^{2} - 7 x + 7$ equal to $0$ .

$x^{2} - 7 x + 7 = 0$

Solve for $x$ .

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Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = - 7$ , and $c = 7$ into the quadratic formula and solve for $x$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (1 \cdot 7)}}{2 \cdot 1}$

Simplify.

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Simplify the numerator.

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Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot (1 \cdot 7)}}{2 \cdot 1}$

Multiply $7$ by $1$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 7}}{2 \cdot 1}$

Multiply $- 4$ by $7$ .

$x = \frac{7 \pm \sqrt{49 - 28}}{2 \cdot 1}$

Subtract $28$ from $49$ .

$x = \frac{7 \pm \sqrt{21}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{7 \pm \sqrt{21}}{2}$

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

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Simplify the numerator.

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Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot (1 \cdot 7)}}{2 \cdot 1}$

Multiply $7$ by $1$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 7}}{2 \cdot 1}$

Multiply $- 4$ by $7$ .

$x = \frac{7 \pm \sqrt{49 - 28}}{2 \cdot 1}$

Subtract $28$ from $49$ .

$x = \frac{7 \pm \sqrt{21}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{7 \pm \sqrt{21}}{2}$

Change the $\pm$ to $+$ .

$x = \frac{7 + \sqrt{21}}{2}$

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

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Simplify the numerator.

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Raise $- 7$ to the power of $2$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot (1 \cdot 7)}}{2 \cdot 1}$

Multiply $7$ by $1$ .

$x = \frac{7 \pm \sqrt{49 - 4 \cdot 7}}{2 \cdot 1}$

Multiply $- 4$ by $7$ .

$x = \frac{7 \pm \sqrt{49 - 28}}{2 \cdot 1}$

Subtract $28$ from $49$ .

$x = \frac{7 \pm \sqrt{21}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{7 \pm \sqrt{21}}{2}$

Change the $\pm$ to $-$ .

$x = \frac{7 - \sqrt{21}}{2}$

The final answer is the combination of both solutions.

$x = \frac{7 + \sqrt{21}}{2}, \frac{7 - \sqrt{21}}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 + \sqrt{21}}{2}, \frac{7 - \sqrt{21}}{2}$

Decimal Form:

$x = 5.79128784 \dots, 1.20871215 \dots$

Find the Roots (Zeros) y=x^2-7x+7

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