How to solve 72=(8x+3)(8x-3)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 72=(8x+3)(8x-3) | Equatix

Question

$$72=(8x+3)(8x-3)$$

Solve for x

$x = \frac{9}{8} = 1\frac{1}{8} = 1.125$
$x = -\frac{9}{8} = -1\frac{1}{8} = -1.125$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Consider $\left(8x+3\right)\left(8x-3\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$. Square $3$.

$$72=\left(8x\right)^{2}-9$$

Expand $\left(8x\right)^{2}$.

$$72=8^{2}x^{2}-9$$

Calculate $8$ to the power of $2$ and get $64$.

$$72=64x^{2}-9$$

Swap sides so that all variable terms are on the left hand side.

$$64x^{2}-9=72$$

Add $9$ to both sides.

$$64x^{2}=72+9$$

Add $72$ and $9$ to get $81$.

$$64x^{2}=81$$

Divide both sides by $64$.

$$x^{2}=\frac{81}{64}$$

Take the square root of both sides of the equation.

$$x=\frac{9}{8}$$ $$x=-\frac{9}{8}$$

Steps Using the Quadratic Formula

Consider $\left(8x+3\right)\left(8x-3\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$. Square $3$.

$$72=\left(8x\right)^{2}-9$$

Expand $\left(8x\right)^{2}$.

$$72=8^{2}x^{2}-9$$

Calculate $8$ to the power of $2$ and get $64$.

$$72=64x^{2}-9$$

Swap sides so that all variable terms are on the left hand side.

$$64x^{2}-9=72$$

Subtract $72$ from both sides.

$$64x^{2}-9-72=0$$

Subtract $72$ from $-9$ to get $-81$.

$$64x^{2}-81=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $64$ for $a$, $0$ for $b$, and $-81$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 64\left(-81\right)}}{2\times 64}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 64\left(-81\right)}}{2\times 64}$$

Multiply $-4$ times $64$.

$$x=\frac{0±\sqrt{-256\left(-81\right)}}{2\times 64}$$

Multiply $-256$ times $-81$.

$$x=\frac{0±\sqrt{20736}}{2\times 64}$$

Take the square root of $20736$.

$$x=\frac{0±144}{2\times 64}$$

Multiply $2$ times $64$.

$$x=\frac{0±144}{128}$$

Now solve the equation $x=\frac{0±144}{128}$ when $±$ is plus. Reduce the fraction $\frac{144}{128}$ to lowest terms by extracting and canceling out $16$.

$$x=\frac{9}{8}$$

Now solve the equation $x=\frac{0±144}{128}$ when $±$ is minus. Reduce the fraction $\frac{-144}{128}$ to lowest terms by extracting and canceling out $16$.

$$x=-\frac{9}{8}$$

The equation is now solved.

$$x=\frac{9}{8}$$ $$x=-\frac{9}{8}$$

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Question

Solve for x

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula