Solve (4x)^2+(3x)^2=37^2

$$( 4 x ) ^ { 2 } + ( 3 x ) ^ { 2 } = 37 ^ { 2 }$$

Solve for x

$$x = -\frac{37}{5} = -7\frac{2}{5} = -7.4$$

$$x = \frac{37}{5} = 7\frac{2}{5} = 7.4$$

Steps Using Difference of Squares

Expand \left(4x\right)^{2}.

$$4^{2}x^{2}+\left(3x\right)^{2}=37^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}+\left(3x\right)^{2}=37^{2}$$

Expand \left(3x\right)^{2}.

$$16x^{2}+3^{2}x^{2}=37^{2}$$

Calculate 3 to the power of 2 and get 9.

$$16x^{2}+9x^{2}=37^{2}$$

Combine 16x^{2} and 9x^{2} to get 25x^{2}.

$$25x^{2}=37^{2}$$

Calculate 37 to the power of 2 and get 1369.

$$25x^{2}=1369$$

Subtract 1369 from both sides.

$$25x^{2}-1369=0$$

Consider 25x^{2}-1369. Rewrite 25x^{2}-1369 as \left(5x\right)^{2}-37^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5x-37\right)\left(5x+37\right)=0$$

To find equation solutions, solve 5x-37=0 and 5x+37=0.

$$x=\frac{37}{5} x=-\frac{37}{5}$$

Steps by Finding Square Root

Expand \left(4x\right)^{2}.

$$4^{2}x^{2}+\left(3x\right)^{2}=37^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}+\left(3x\right)^{2}=37^{2}$$

Expand \left(3x\right)^{2}.

$$16x^{2}+3^{2}x^{2}=37^{2}$$

Calculate 3 to the power of 2 and get 9.

$$16x^{2}+9x^{2}=37^{2}$$

Combine 16x^{2} and 9x^{2} to get 25x^{2}.

$$25x^{2}=37^{2}$$

Calculate 37 to the power of 2 and get 1369.

$$25x^{2}=1369$$

Divide both sides by 25.

$$x^{2}=\frac{1369}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{37}{5} x=-\frac{37}{5}$$

Steps Using the Quadratic Formula

Expand \left(4x\right)^{2}.

$$4^{2}x^{2}+\left(3x\right)^{2}=37^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}+\left(3x\right)^{2}=37^{2}$$

Expand \left(3x\right)^{2}.

$$16x^{2}+3^{2}x^{2}=37^{2}$$

Calculate 3 to the power of 2 and get 9.

$$16x^{2}+9x^{2}=37^{2}$$

Combine 16x^{2} and 9x^{2} to get 25x^{2}.

$$25x^{2}=37^{2}$$

Calculate 37 to the power of 2 and get 1369.

$$25x^{2}=1369$$

Subtract 1369 from both sides.

$$25x^{2}-1369=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and -1369 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\left(-1369\right)}}{2\times 25}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 25\left(-1369\right)}}{2\times 25}$$

Multiply -4 times 25.

$$x=\frac{0±\sqrt{-100\left(-1369\right)}}{2\times 25}$$

Multiply -100 times -1369.

$$x=\frac{0±\sqrt{136900}}{2\times 25}$$

Take the square root of 136900.

$$x=\frac{0±370}{2\times 25}$$

Multiply 2 times 25.

$$x=\frac{0±370}{50}$$

Now solve the equation x=\frac{0±370}{50} when ± is plus. Reduce the fraction \frac{370}{50} to lowest terms by extracting and canceling out 10.

$$x=\frac{37}{5}$$

Now solve the equation x=\frac{0±370}{50} when ± is minus. Reduce the fraction \frac{-370}{50} to lowest terms by extracting and canceling out 10.

$$x=-\frac{37}{5}$$

The equation is now solved.

$$x=\frac{37}{5} x=-\frac{37}{5}$$