Solve 3(x)^(2)-5=2(x)^(2)+11 | 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

$$3 { x }^{ 2 } -5=2 { x }^{ 2 } +11$$

Solve for x

$x=4$
$x=-4$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

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

$$3x^{2}-5-2x^{2}=11$$

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

$$x^{2}-5=11$$

Subtract $11$ from both sides.

$$x^{2}-5-11=0$$

Subtract $11$ from $-5$ to get $-16$.

$$x^{2}-16=0$$

Consider $x^{2}-16$. Rewrite $x^{2}-16$ as $x^{2}-4^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(x-4\right)\left(x+4\right)=0$$

To find equation solutions, solve $x-4=0$ and $x+4=0$.

$$x=4$$ $$x=-4$$

Steps by Finding Square Root

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

$$3x^{2}-5-2x^{2}=11$$

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

$$x^{2}-5=11$$

Add $5$ to both sides.

$$x^{2}=11+5$$

Add $11$ and $5$ to get $16$.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4$$ $$x=-4$$

Steps Using the Quadratic Formula

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

$$3x^{2}-5-2x^{2}=11$$

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

$$x^{2}-5=11$$

Subtract $11$ from both sides.

$$x^{2}-5-11=0$$

Subtract $11$ from $-5$ to get $-16$.

$$x^{2}-16=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-16$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-16\right)}}{2}$$

Multiply $-4$ times $-16$.

$$x=\frac{0±\sqrt{64}}{2}$$

Take the square root of $64$.

$$x=\frac{0±8}{2}$$

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

$$x=4$$

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

$$x=-4$$

The equation is now solved.

$$x=4$$ $$x=-4$$