Solve x(x+4)-3=4(x+19.5)

$$x ( x + 4 ) - 3 = 4 ( x + 19.5 )$$

Solve for x

$$x=-9$$

$$x=9$$

Steps by Finding Square Root

Use the distributive property to multiply x by x+4.

$$x^{2}+4x-3=4\left(x+19.5\right)$$

Use the distributive property to multiply 4 by x+19.5.

$$x^{2}+4x-3=4x+78$$

Subtract 4x from both sides.

$$x^{2}+4x-3-4x=78$$

Combine 4x and -4x to get 0.

$$x^{2}-3=78$$

Add 3 to both sides.

$$x^{2}=78+3$$

Add 78 and 3 to get 81.

$$x^{2}=81$$

Take the square root of both sides of the equation.

$$x=9 x=-9$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x+4.

$$x^{2}+4x-3=4\left(x+19.5\right)$$

Use the distributive property to multiply 4 by x+19.5.

$$x^{2}+4x-3=4x+78$$

Subtract 4x from both sides.

$$x^{2}+4x-3-4x=78$$

Combine 4x and -4x to get 0.

$$x^{2}-3=78$$

Subtract 78 from both sides.

$$x^{2}-3-78=0$$

Subtract 78 from -3 to get -81.

$$x^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

Multiply -4 times -81.

$$x=\frac{0±\sqrt{324}}{2}$$

Take the square root of 324.

$$x=\frac{0±18}{2}$$

Now solve the equation x=\frac{0±18}{2} when ± is plus. Divide 18 by 2.

$$x=9$$

Now solve the equation x=\frac{0±18}{2} when ± is minus. Divide -18 by 2.

$$x=-9$$

The equation is now solved.

$$x=9 x=-9$$