Solve (x-2)(x+3)=x+19

$$(x-2)(x+3)=x+19$$

Solve for x

$$x=-5$$

$$x=5$$

Steps by Finding Square Root

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

$$x^{2}+x-6=x+19$$

Subtract x from both sides.

$$x^{2}+x-6-x=19$$

Combine x and -x to get 0.

$$x^{2}-6=19$$

Add 6 to both sides.

$$x^{2}=19+6$$

Add 19 and 6 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 x-2 by x+3 and combine like terms.

$$x^{2}+x-6=x+19$$

Subtract x from both sides.

$$x^{2}+x-6-x=19$$

Combine x and -x to get 0.

$$x^{2}-6=19$$

Subtract 19 from both sides.

$$x^{2}-6-19=0$$

Subtract 19 from -6 to get -25.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -25.

$$x=\frac{0±\sqrt{100}}{2}$$

Take the square root of 100.

$$x=\frac{0±10}{2}$$

Now solve the equation x=\frac{0±10}{2} when ± is plus. Divide 10 by 2.

$$x=5$$

Now solve the equation x=\frac{0±10}{2} when ± is minus. Divide -10 by 2.

$$x=-5$$

The equation is now solved.

$$x=5 x=-5$$