Solve 115 ^ 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

$$115^{2}+x^{2}=196^{2}$$

Solve for x

$x=9\sqrt{311}\approx 158.716728797$
$x=-9\sqrt{311}\approx -158.716728797$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Calculate $115$ to the power of $2$ and get $13225$.

$$13225+x^{2}=196^{2}$$

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

$$13225+x^{2}=38416$$

Subtract $13225$ from both sides.

$$x^{2}=38416-13225$$

Subtract $13225$ from $38416$ to get $25191$.

$$x^{2}=25191$$

Take the square root of both sides of the equation.

$$x=9\sqrt{311}$$ $$x=-9\sqrt{311}$$

Steps Using the Quadratic Formula

Calculate $115$ to the power of $2$ and get $13225$.

$$13225+x^{2}=196^{2}$$

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

$$13225+x^{2}=38416$$

Subtract $38416$ from both sides.

$$13225+x^{2}-38416=0$$

Subtract $38416$ from $13225$ to get $-25191$.

$$-25191+x^{2}=0$$

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

$$x^{2}-25191=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-25191$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-25191\right)}}{2}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-25191\right)}}{2}$$

Multiply $-4$ times $-25191$.

$$x=\frac{0±\sqrt{100764}}{2}$$

Take the square root of $100764$.

$$x=\frac{0±18\sqrt{311}}{2}$$

Now solve the equation $x=\frac{0±18\sqrt{311}}{2}$ when $±$ is plus.

$$x=9\sqrt{311}$$

Now solve the equation $x=\frac{0±18\sqrt{311}}{2}$ when $±$ is minus.

$$x=-9\sqrt{311}$$

The equation is now solved.

$$x=9\sqrt{311}$$ $$x=-9\sqrt{311}$$