Solve (2x+4)^2-(x-5)^2=26x

$$( 2 x + 4 ) ^ { 2 } - ( x - 5 ) ^ { 2 } = 26 x$$

Solve for x

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

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

$$4x^{2}+16x+16-\left(x-5\right)^{2}=26x$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$4x^{2}+16x+16-\left(x^{2}-10x+25\right)=26x$$

To find the opposite of x^{2}-10x+25, find the opposite of each term.

$$4x^{2}+16x+16-x^{2}+10x-25=26x$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}+16x+16+10x-25=26x$$

Combine 16x and 10x to get 26x.

$$3x^{2}+26x+16-25=26x$$

Subtract 25 from 16 to get -9.

$$3x^{2}+26x-9=26x$$

Subtract 26x from both sides.

$$3x^{2}+26x-9-26x=0$$

Combine 26x and -26x to get 0.

$$3x^{2}-9=0$$

Add 9 to both sides. Anything plus zero gives itself.

$$3x^{2}=9$$

Divide both sides by 3.

$$x^{2}=\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$x^{2}=3$$

Take the square root of both sides of the equation.

$$x=\sqrt{3} x=-\sqrt{3}$$

Steps Using the Quadratic Formula

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

$$4x^{2}+16x+16-\left(x-5\right)^{2}=26x$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$4x^{2}+16x+16-\left(x^{2}-10x+25\right)=26x$$

To find the opposite of x^{2}-10x+25, find the opposite of each term.

$$4x^{2}+16x+16-x^{2}+10x-25=26x$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}+16x+16+10x-25=26x$$

Combine 16x and 10x to get 26x.

$$3x^{2}+26x+16-25=26x$$

Subtract 25 from 16 to get -9.

$$3x^{2}+26x-9=26x$$

Subtract 26x from both sides.

$$3x^{2}+26x-9-26x=0$$

Combine 26x and -26x to get 0.

$$3x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-9\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-9\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-9\right)}}{2\times 3}$$

Multiply -12 times -9.

$$x=\frac{0±\sqrt{108}}{2\times 3}$$

Take the square root of 108.

$$x=\frac{0±6\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±6\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±6\sqrt{3}}{6} when ± is plus.

$$x=\sqrt{3}$$

Now solve the equation x=\frac{0±6\sqrt{3}}{6} when ± is minus.

$$x=-\sqrt{3}$$

The equation is now solved.

$$x=\sqrt{3} x=-\sqrt{3}$$