Solve 5(x)^(2)-7=5+2(x)^(2) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$5 { x }^{ 2 } -7=5+2 { x }^{ 2 }$$

Solve for x

$x=2$
$x=-2$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Subtract $5$ from both sides.

$$5x^{2}-7-5=2x^{2}$$

Subtract $5$ from $-7$ to get $-12$.

$$5x^{2}-12=2x^{2}$$

Subtract $2x^{2}$ from both sides.

$$5x^{2}-12-2x^{2}=0$$

Combine $5x^{2}$ and $-2x^{2}$ to get $3x^{2}$.

$$3x^{2}-12=0$$

Divide both sides by $3$.

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

Consider $x^{2}-4$. Rewrite $x^{2}-4$ as $x^{2}-2^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(x-2\right)\left(x+2\right)=0$$

To find equation solutions, solve $x-2=0$ and $x+2=0$.

$$x=2$$ $$x=-2$$

Steps by Finding Square Root

Subtract $2x^{2}$ from both sides.

$$5x^{2}-7-2x^{2}=5$$

Combine $5x^{2}$ and $-2x^{2}$ to get $3x^{2}$.

$$3x^{2}-7=5$$

Add $7$ to both sides.

$$3x^{2}=5+7$$

Add $5$ and $7$ to get $12$.

$$3x^{2}=12$$

Divide both sides by $3$.

$$x^{2}=\frac{12}{3}$$

Divide $12$ by $3$ to get $4$.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2$$ $$x=-2$$

Steps Using the Quadratic Formula

Subtract $5$ from both sides.

$$5x^{2}-7-5=2x^{2}$$

Subtract $5$ from $-7$ to get $-12$.

$$5x^{2}-12=2x^{2}$$

Subtract $2x^{2}$ from both sides.

$$5x^{2}-12-2x^{2}=0$$

Combine $5x^{2}$ and $-2x^{2}$ to get $3x^{2}$.

$$3x^{2}-12=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $3$ for $a$, $0$ for $b$, and $-12$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-12\right)}}{2\times 3}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\times 3\left(-12\right)}}{2\times 3}$$

Multiply $-4$ times $3$.

$$x=\frac{0±\sqrt{-12\left(-12\right)}}{2\times 3}$$

Multiply $-12$ times $-12$.

$$x=\frac{0±\sqrt{144}}{2\times 3}$$

Take the square root of $144$.

$$x=\frac{0±12}{2\times 3}$$

Multiply $2$ times $3$.

$$x=\frac{0±12}{6}$$

Now solve the equation $x=\frac{0±12}{6}$ when $±$ is plus. Divide $12$ by $6$.

$$x=2$$

Now solve the equation $x=\frac{0±12}{6}$ when $±$ is minus. Divide $-12$ by $6$.

$$x=-2$$

The equation is now solved.

$$x=2$$ $$x=-2$$