Algebra Examples

$y = {(3 x - 4)}^{2}$

To find the roots of the equation, replace $y$ with $0$ and solve.

$0 = 9 x^{2} - 24 x + 16$

Rewrite the equation as $9 x^{2} - 24 x + 16 = 0$ .

$9 x^{2} - 24 x + 16 = 0$

Factor using the perfect square rule.

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Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

${(3 x)}^{2} - 24 x + 16 = 0$

Rewrite $16$ as $4^{2}$ .

${(3 x)}^{2} - 24 x + 4^{2} = 0$

Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot (3 x) \cdot - 4$

Simplify.

$2 a b = - 24 x$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 3 x$ and $b = - 4$ .

${(3 x - 4)}^{2} = 0$

Set $3 x - 4$ equal to $0$ and solve for $x$ .

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Set the factor equal to $0$ .

$3 x - 4 = 0$

Add $4$ to both sides of the equation.

$3 x = 4$

Divide each term by $3$ and simplify.

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Divide each term in $3 x = 4$ by $3$ .

$\frac{3 x}{3} = \frac{4}{3}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$\frac{3 x}{3} = \frac{4}{3}$

Divide $x$ by $1$ .

$x = \frac{4}{3}$

The solution is the result of $3 x - 4 = 0$ .

$x = \frac{4}{3}$

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