Solve left(2x-3right)left(x+7right)+left(2x+3right)left(x-7right)=58

$$\left( 2x-3 \right) \left( x+7 \right) + \left( 2x+3 \right) \left( x-7 \right) = 58$$

Solve for x

$$x=-5$$

$$x=5$$

Steps by Finding Square Root

Use the distributive property to multiply 2x-3 by x+7 and combine like terms.

$$2x^{2}+11x-21+\left(2x+3\right)\left(x-7\right)=58$$

Use the distributive property to multiply 2x+3 by x-7 and combine like terms.

$$2x^{2}+11x-21+2x^{2}-11x-21=58$$

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

$$4x^{2}+11x-21-11x-21=58$$

Combine 11x and -11x to get 0.

$$4x^{2}-21-21=58$$

Subtract 21 from -21 to get -42.

$$4x^{2}-42=58$$

Add 42 to both sides.

$$4x^{2}=58+42$$

Add 58 and 42 to get 100.

$$4x^{2}=100$$

Divide both sides by 4.

$$x^{2}=\frac{100}{4}$$

Divide 100 by 4 to get 25.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x-3 by x+7 and combine like terms.

$$2x^{2}+11x-21+\left(2x+3\right)\left(x-7\right)=58$$

Use the distributive property to multiply 2x+3 by x-7 and combine like terms.

$$2x^{2}+11x-21+2x^{2}-11x-21=58$$

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

$$4x^{2}+11x-21-11x-21=58$$

Combine 11x and -11x to get 0.

$$4x^{2}-21-21=58$$

Subtract 21 from -21 to get -42.

$$4x^{2}-42=58$$

Subtract 58 from both sides.

$$4x^{2}-42-58=0$$

Subtract 58 from -42 to get -100.

$$4x^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-100\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-100\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-100\right)}}{2\times 4}$$

Multiply -16 times -100.

$$x=\frac{0±\sqrt{1600}}{2\times 4}$$

Take the square root of 1600.

$$x=\frac{0±40}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±40}{8}$$

Now solve the equation x=\frac{0±40}{8} when ± is plus. Divide 40 by 8.

$$x=5$$

Now solve the equation x=\frac{0±40}{8} when ± is minus. Divide -40 by 8.

$$x=-5$$

The equation is now solved.

$$x=5 x=-5$$