Solve 5 ^ 2 + x ^ 2 = 196 ^ 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

$$57.5^{2}+x^{2}=196^{2}$$

Solve for x

$x = \frac{13 \sqrt{831}}{2} \approx 187.37595897$
$x = -\frac{13 \sqrt{831}}{2} \approx -187.37595897$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Calculate $57.5$ to the power of $2$ and get $3306.25$.

$$3306.25+x^{2}=196^{2}$$

Calculate $196$ to the power of $2$ and get $38416$.

$$3306.25+x^{2}=38416$$

Subtract $3306.25$ from both sides.

$$x^{2}=38416-3306.25$$

Subtract $3306.25$ from $38416$ to get $35109.75$.

$$x^{2}=35109.75$$

Take the square root of both sides of the equation.

$$x=\frac{13\sqrt{831}}{2}$$ $$x=-\frac{13\sqrt{831}}{2}$$

Steps Using the Quadratic Formula

Calculate $57.5$ to the power of $2$ and get $3306.25$.

$$3306.25+x^{2}=196^{2}$$

Calculate $196$ to the power of $2$ and get $38416$.

$$3306.25+x^{2}=38416$$

Subtract $38416$ from both sides.

$$3306.25+x^{2}-38416=0$$

Subtract $38416$ from $3306.25$ to get $-35109.75$.

$$-35109.75+x^{2}=0$$

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: $ax^{2}+bx+c=0$.

$$x^{2}-35109.75=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-35109.75$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-35109.75\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-35109.75\right)}}{2}$$

Multiply $-4$ times $-35109.75$.

$$x=\frac{0±\sqrt{140439}}{2}$$

Take the square root of $140439$.

$$x=\frac{0±13\sqrt{831}}{2}$$

Now solve the equation $x=\frac{0±13\sqrt{831}}{2}$ when $±$ is plus.

$$x=\frac{13\sqrt{831}}{2}$$

Now solve the equation $x=\frac{0±13\sqrt{831}}{2}$ when $±$ is minus.

$$x=-\frac{13\sqrt{831}}{2}$$

The equation is now solved.

$$x=\frac{13\sqrt{831}}{2}$$ $$x=-\frac{13\sqrt{831}}{2}$$