How to solve 36 - x ^ 2 = 4

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 36 - x ^ 2 = 4 | Equatix

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Question

$$36-x^{2}=4$$

Solve for x

$x=4\sqrt{2}\approx 5.656854249$
$x=-4\sqrt{2}\approx -5.656854249$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Subtract $36$ from both sides.

$$-x^{2}=4-36$$

Subtract $36$ from $4$ to get $-32$.

$$-x^{2}=-32$$

Divide both sides by $-1$.

$$x^{2}=\frac{-32}{-1}$$

Fraction $\frac{-32}{-1}$ can be simplified to $32$ by removing the negative sign from both the numerator and the denominator.

$$x^{2}=32$$

Take the square root of both sides of the equation.

$$x=4\sqrt{2}$$ $$x=-4\sqrt{2}$$

Steps Using the Quadratic Formula

Subtract $4$ from both sides.

$$36-x^{2}-4=0$$

Subtract $4$ from $36$ to get $32$.

$$32-x^{2}=0$$

Quadratic equations like this one, with an $x^{2}$ term but no $x$ term, can still be solved using the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$, once they are put in standard form: $ax^{2}+bx+c=0$.

$$-x^{2}+32=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-1$ for $a$, $0$ for $b$, and $32$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 32}}{2\left(-1\right)}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 32}}{2\left(-1\right)}$$

Multiply $-4$ times $-1$.

$$x=\frac{0±\sqrt{4\times 32}}{2\left(-1\right)}$$

Multiply $4$ times $32$.

$$x=\frac{0±\sqrt{128}}{2\left(-1\right)}$$

Take the square root of $128$.

$$x=\frac{0±8\sqrt{2}}{2\left(-1\right)}$$

Multiply $2$ times $-1$.

$$x=\frac{0±8\sqrt{2}}{-2}$$

Now solve the equation $x=\frac{0±8\sqrt{2}}{-2}$ when $±$ is plus.

$$x=-4\sqrt{2}$$

Now solve the equation $x=\frac{0±8\sqrt{2}}{-2}$ when $±$ is minus.

$$x=4\sqrt{2}$$

The equation is now solved.

$$x=-4\sqrt{2}$$ $$x=4\sqrt{2}$$

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Basic Math

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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