Solve (-4x-2)^2+(2-4x)^2=50

$$( - 4 x - 2 ) ^ { 2 } + ( 2 - 4 x ) ^ { 2 } = 50$$

Solve for x

$$x = -\frac{\sqrt{21}}{4} \approx -1.145643924$$

$$x = \frac{\sqrt{21}}{4} \approx 1.145643924$$

Steps by Finding Square Root

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-4x-2\right)^{2}.

$$16x^{2}+16x+4+\left(2-4x\right)^{2}=50$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2-4x\right)^{2}.

$$16x^{2}+16x+4+4-16x+16x^{2}=50$$

Add 4 and 4 to get 8.

$$16x^{2}+16x+8-16x+16x^{2}=50$$

Combine 16x and -16x to get 0.

$$16x^{2}+8+16x^{2}=50$$

Combine 16x^{2} and 16x^{2} to get 32x^{2}.

$$32x^{2}+8=50$$

Subtract 8 from both sides.

$$32x^{2}=50-8$$

Subtract 8 from 50 to get 42.

$$32x^{2}=42$$

Divide both sides by 32.

$$x^{2}=\frac{42}{32}$$

Reduce the fraction \frac{42}{32} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{21}{16}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{21}}{4} x=-\frac{\sqrt{21}}{4}$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-4x-2\right)^{2}.

$$16x^{2}+16x+4+\left(2-4x\right)^{2}=50$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2-4x\right)^{2}.

$$16x^{2}+16x+4+4-16x+16x^{2}=50$$

Add 4 and 4 to get 8.

$$16x^{2}+16x+8-16x+16x^{2}=50$$

Combine 16x and -16x to get 0.

$$16x^{2}+8+16x^{2}=50$$

Combine 16x^{2} and 16x^{2} to get 32x^{2}.

$$32x^{2}+8=50$$

Subtract 50 from both sides.

$$32x^{2}+8-50=0$$

Subtract 50 from 8 to get -42.

$$32x^{2}-42=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 32 for a, 0 for b, and -42 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 32\left(-42\right)}}{2\times 32}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 32\left(-42\right)}}{2\times 32}$$

Multiply -4 times 32.

$$x=\frac{0±\sqrt{-128\left(-42\right)}}{2\times 32}$$

Multiply -128 times -42.

$$x=\frac{0±\sqrt{5376}}{2\times 32}$$

Take the square root of 5376.

$$x=\frac{0±16\sqrt{21}}{2\times 32}$$

Multiply 2 times 32.

$$x=\frac{0±16\sqrt{21}}{64}$$

Now solve the equation x=\frac{0±16\sqrt{21}}{64} when ± is plus.

$$x=\frac{\sqrt{21}}{4}$$

Now solve the equation x=\frac{0±16\sqrt{21}}{64} when ± is minus.

$$x=-\frac{\sqrt{21}}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{21}}{4} x=-\frac{\sqrt{21}}{4}$$