Solve (2x-1)(x+5)=9x+13

$$( 2 x - 1 ) ( x + 5 ) = 9 x + 13$$

Solve for x

$$x=-3$$

$$x=3$$

Steps by Finding Square Root

Use the distributive property to multiply 2x-1 by x+5 and combine like terms.

$$2x^{2}+9x-5=9x+13$$

Subtract 9x from both sides.

$$2x^{2}+9x-5-9x=13$$

Combine 9x and -9x to get 0.

$$2x^{2}-5=13$$

Add 5 to both sides.

$$2x^{2}=13+5$$

Add 13 and 5 to get 18.

$$2x^{2}=18$$

Divide both sides by 2.

$$x^{2}=\frac{18}{2}$$

Divide 18 by 2 to get 9.

$$x^{2}=9$$

Take the square root of both sides of the equation.

$$x=3 x=-3$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x-1 by x+5 and combine like terms.

$$2x^{2}+9x-5=9x+13$$

Subtract 9x from both sides.

$$2x^{2}+9x-5-9x=13$$

Combine 9x and -9x to get 0.

$$2x^{2}-5=13$$

Subtract 13 from both sides.

$$2x^{2}-5-13=0$$

Subtract 13 from -5 to get -18.

$$2x^{2}-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-18\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-18\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-18\right)}}{2\times 2}$$

Multiply -8 times -18.

$$x=\frac{0±\sqrt{144}}{2\times 2}$$

Take the square root of 144.

$$x=\frac{0±12}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±12}{4}$$

Now solve the equation x=\frac{0±12}{4} when ± is plus. Divide 12 by 4.

$$x=3$$

Now solve the equation x=\frac{0±12}{4} when ± is minus. Divide -12 by 4.

$$x=-3$$

The equation is now solved.

$$x=3 x=-3$$