Solve (x-7)*(x+3)=24

$$( x - 7 ) \cdot ( x + 3 ) = 24$$

Solve for x

$$x=-5$$

$$x=9$$

Steps Using the Quadratic Formula

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

$$x^{2}-4x-21=24$$

Subtract 24 from both sides.

$$x^{2}-4x-21-24=0$$

Subtract 24 from -21 to get -45.

$$x^{2}-4x-45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -4 for b, and -45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-45\right)}}{2}$$

Square -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-45\right)}}{2}$$

Multiply -4 times -45.

$$x=\frac{-\left(-4\right)±\sqrt{16+180}}{2}$$

Add 16 to 180.

$$x=\frac{-\left(-4\right)±\sqrt{196}}{2}$$

Take the square root of 196.

$$x=\frac{-\left(-4\right)±14}{2}$$

The opposite of -4 is 4.

$$x=\frac{4±14}{2}$$

Now solve the equation x=\frac{4±14}{2} when ± is plus. Add 4 to 14.

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

Divide 18 by 2.

$$x=9$$

Now solve the equation x=\frac{4±14}{2} when ± is minus. Subtract 14 from 4.

$$x=-\frac{10}{2}$$

Divide -10 by 2.

$$x=-5$$

The equation is now solved.

$$x=9 x=-5$$

Steps for Completing the Square

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

$$x^{2}-4x-21=24$$

Add 21 to both sides.

$$x^{2}-4x=24+21$$

Add 24 and 21 to get 45.

$$x^{2}-4x=45$$

Divide -4, the coefficient of the x term, by 2 to get -2. Then add the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-4x+\left(-2\right)^{2}=45+\left(-2\right)^{2}$$

Square -2.

$$x^{2}-4x+4=45+4$$

Add 45 to 4.

$$x^{2}-4x+4=49$$

Factor x^{2}-4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-2\right)^{2}=49$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{49}$$

Simplify.

$$x-2=7 x-2=-7$$

Add 2 to both sides of the equation.

$$x=9 x=-5$$