Solve Using the Square Root Property 16x^2=56x

$16 x^{2} = 56 x$

Subtract $56 x$ from both sides of the equation.

$16 x^{2} - 56 x = 0$

Factor $8 x$ out of $16 x^{2} - 56 x$ .

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Factor $8 x$ out of $16 x^{2}$ .

$8 x (2 x) - 56 x = 0$

Factor $8 x$ out of $- 56 x$ .

$8 x (2 x) + 8 x (- 7) = 0$

Factor $8 x$ out of $8 x (2 x) + 8 x (- 7)$ .

$8 x (2 x - 7) = 0$

Divide each term by $8$ and simplify.

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Divide each term in $8 x (2 x - 7) = 0$ by $8$ .

$\frac{8 x (2 x - 7)}{8} = \frac{0}{8}$

Simplify $\frac{8 x (2 x - 7)}{8}$ .

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Simplify terms.

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Cancel the common factor of $8$ .

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Cancel the common factor.

$\frac{8 x (2 x - 7)}{8} = \frac{0}{8}$

Divide $x (2 x - 7)$ by $1$ .

$x (2 x - 7) = \frac{0}{8}$

Apply the distributive property.

$x (2 x) + x \cdot - 7 = \frac{0}{8}$

Reorder.

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Rewrite using the commutative property of multiplication.

$2 x \cdot x + x \cdot - 7 = \frac{0}{8}$

Move $- 7$ to the left of $x$ .

$2 x \cdot x - 7 \cdot x = \frac{0}{8}$

Multiply $x$ by $x$ by adding the exponents.

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Move $x$ .

$2 (x \cdot x) - 7 \cdot x = \frac{0}{8}$

Multiply $x$ by $x$ .

$2 x^{2} - 7 \cdot x = \frac{0}{8}$

$2 x^{2} - 7 x = \frac{0}{8}$

Divide $0$ by $8$ .

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

Factor $x$ out of $2 x^{2} - 7 x$ .

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

$x (2 x) - 7 x = 0$

Factor $x$ out of $- 7 x$ .

$x (2 x) + x \cdot - 7 = 0$

Factor $x$ out of $x (2 x) + x \cdot - 7$ .

$x (2 x - 7) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$2 x - 7 = 0$

Set the first factor equal to $0$ .

$x = 0$

Set the next factor equal to $0$ and solve.

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Set the next factor equal to $0$ .

$2 x - 7 = 0$

Add $7$ to both sides of the equation.

$2 x = 7$

Divide each term by $2$ and simplify.

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Divide each term in $2 x = 7$ by $2$ .

$\frac{2 x}{2} = \frac{7}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 x}{2} = \frac{7}{2}$

Divide $x$ by $1$ .

$x = \frac{7}{2}$

The final solution is all the values that make $x (2 x - 7) = 0$ true.

$x = 0, \frac{7}{2}$

Solve Using the Square Root Property 16x^2=56x

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