Solve (x)^(2)=(2.5)^(2)+36 | 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

$${ x }^{ 2 } = { 2.5 }^{ 2 } +36$$

Solve for x

$x=6.5$
$x=-6.5$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Calculate $2.5$ to the power of $2$ and get $6.25$.

$$x^{2}=6.25+36$$

Add $6.25$ and $36$ to get $42.25$.

$$x^{2}=42.25$$

Subtract $42.25$ from both sides.

$$x^{2}-42.25=0$$

Consider $x^{2}-42.25$. Rewrite $x^{2}-42.25$ as $x^{2}-\left(\frac{13}{2}\right)^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(x-\frac{13}{2}\right)\left(x+\frac{13}{2}\right)=0$$

To find equation solutions, solve $x-\frac{13}{2}=0$ and $x+\frac{13}{2}=0$.

$$x=\frac{13}{2}$$ $$x=-\frac{13}{2}$$

Steps by Finding Square Root

Calculate $2.5$ to the power of $2$ and get $6.25$.

$$x^{2}=6.25+36$$

Add $6.25$ and $36$ to get $42.25$.

$$x^{2}=42.25$$

Take the square root of both sides of the equation.

$$x=\frac{13}{2}$$ $$x=-\frac{13}{2}$$

Steps Using the Quadratic Formula

Calculate $2.5$ to the power of $2$ and get $6.25$.

$$x^{2}=6.25+36$$

Add $6.25$ and $36$ to get $42.25$.

$$x^{2}=42.25$$

Subtract $42.25$ from both sides.

$$x^{2}-42.25=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-42.25$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-42.25\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-42.25\right)}}{2}$$

Multiply $-4$ times $-42.25$.

$$x=\frac{0±\sqrt{169}}{2}$$

Take the square root of $169$.

$$x=\frac{0±13}{2}$$

Now solve the equation $x=\frac{0±13}{2}$ when $±$ is plus. Divide $13$ by $2$.

$$x=\frac{13}{2}$$

Now solve the equation $x=\frac{0±13}{2}$ when $±$ is minus. Divide $-13$ by $2$.

$$x=-\frac{13}{2}$$

The equation is now solved.

$$x=\frac{13}{2}$$ $$x=-\frac{13}{2}$$