Solve 25 ^ 2 = L ^ 2 * 7 ^ 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

$$25^{2}=L^{2}\times7^{2}$$

Solve for L

$L = \frac{25}{7} = 3\frac{4}{7} \approx 3.571428571$
$L = -\frac{25}{7} = -3\frac{4}{7} \approx -3.571428571$

Steps Using Difference of Squares

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps Using Difference of Squares

Calculate $25$ to the power of $2$ and get $625$.

$$625=L^{2}\times 7^{2}$$

Calculate $7$ to the power of $2$ and get $49$.

$$625=L^{2}\times 49$$

Swap sides so that all variable terms are on the left hand side.

$$L^{2}\times 49=625$$

Subtract $625$ from both sides.

$$L^{2}\times 49-625=0$$

Consider $L^{2}\times 49-625$. Rewrite $L^{2}\times 49-625$ as $\left(7L\right)^{2}-25^{2}$. The difference of squares can be factored using the rule: $a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$.

$$\left(7L-25\right)\left(7L+25\right)=0$$

To find equation solutions, solve $7L-25=0$ and $7L+25=0$.

$$L=\frac{25}{7}$$ $$L=-\frac{25}{7}$$

Steps by Finding Square Root

Calculate $25$ to the power of $2$ and get $625$.

$$625=L^{2}\times 7^{2}$$

Calculate $7$ to the power of $2$ and get $49$.

$$625=L^{2}\times 49$$

Swap sides so that all variable terms are on the left hand side.

$$L^{2}\times 49=625$$

Divide both sides by $49$.

$$L^{2}=\frac{625}{49}$$

Take the square root of both sides of the equation.

$$L=\frac{25}{7}$$ $$L=-\frac{25}{7}$$

Steps Using the Quadratic Formula

Calculate $25$ to the power of $2$ and get $625$.

$$625=L^{2}\times 7^{2}$$

Calculate $7$ to the power of $2$ and get $49$.

$$625=L^{2}\times 49$$

Swap sides so that all variable terms are on the left hand side.

$$L^{2}\times 49=625$$

Subtract $625$ from both sides.

$$L^{2}\times 49-625=0$$

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

$$49L^{2}-625=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $49$ for $a$, $0$ for $b$, and $-625$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$L=\frac{0±\sqrt{0^{2}-4\times 49\left(-625\right)}}{2\times 49}$$

Square $0$.

$$L=\frac{0±\sqrt{-4\times 49\left(-625\right)}}{2\times 49}$$

Multiply $-4$ times $49$.

$$L=\frac{0±\sqrt{-196\left(-625\right)}}{2\times 49}$$

Multiply $-196$ times $-625$.

$$L=\frac{0±\sqrt{122500}}{2\times 49}$$

Take the square root of $122500$.

$$L=\frac{0±350}{2\times 49}$$

Multiply $2$ times $49$.

$$L=\frac{0±350}{98}$$

Now solve the equation $L=\frac{0±350}{98}$ when $±$ is plus. Reduce the fraction $\frac{350}{98}$ to lowest terms by extracting and canceling out $14$.

$$L=\frac{25}{7}$$

Now solve the equation $L=\frac{0±350}{98}$ when $±$ is minus. Reduce the fraction $\frac{-350}{98}$ to lowest terms by extracting and canceling out $14$.

$$L=-\frac{25}{7}$$

The equation is now solved.

$$L=\frac{25}{7}$$ $$L=-\frac{25}{7}$$