How to solve 9(x)^(2)-49-42=0

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 9(x)^(2)-49-42=0 | Equatix

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Question

$$9 { x }^{ 2 } -49-42=0$$

Solve for x

$x = \frac{\sqrt{91}}{3} \approx 3.179797338$
$x = -\frac{\sqrt{91}}{3} \approx -3.179797338$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Subtract $42$ from $-49$ to get $-91$.

$$9x^{2}-91=0$$

Add $91$ to both sides. Anything plus zero gives itself.

$$9x^{2}=91$$

Divide both sides by $9$.

$$x^{2}=\frac{91}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{91}}{3}$$ $$x=-\frac{\sqrt{91}}{3}$$

Steps Using the Quadratic Formula

Subtract $42$ from $-49$ to get $-91$.

$$9x^{2}-91=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $9$ for $a$, $0$ for $b$, and $-91$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-91\right)}}{2\times 9}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 9\left(-91\right)}}{2\times 9}$$

Multiply $-4$ times $9$.

$$x=\frac{0±\sqrt{-36\left(-91\right)}}{2\times 9}$$

Multiply $-36$ times $-91$.

$$x=\frac{0±\sqrt{3276}}{2\times 9}$$

Take the square root of $3276$.

$$x=\frac{0±6\sqrt{91}}{2\times 9}$$

Multiply $2$ times $9$.

$$x=\frac{0±6\sqrt{91}}{18}$$

Now solve the equation $x=\frac{0±6\sqrt{91}}{18}$ when $±$ is plus.

$$x=\frac{\sqrt{91}}{3}$$

Now solve the equation $x=\frac{0±6\sqrt{91}}{18}$ when $±$ is minus.

$$x=-\frac{\sqrt{91}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{91}}{3}$$ $$x=-\frac{\sqrt{91}}{3}$$

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Example

Question

Solve for x

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula