Solve x^2+3x+9/4=0

$$x ^ { 2 } + 3 x + \frac { 9 } { 4 } = 0$$

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps Using the Quadratic Formula

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x^{2}+3x+\frac{9}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 3 for b, and \frac{9}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3±\sqrt{3^{2}-4\times \frac{9}{4}}}{2}$$

Square 3.

$$x=\frac{-3±\sqrt{9-4\times \frac{9}{4}}}{2}$$

Multiply -4 times \frac{9}{4}.

$$x=\frac{-3±\sqrt{9-9}}{2}$$

Add 9 to -9.

$$x=\frac{-3±\sqrt{0}}{2}$$

Take the square root of 0.

$$x=-\frac{3}{2}$$

Steps for Completing the Square

Factor x^{2}+3x+\frac{9}{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}.

$$\left(x+\frac{3}{2}\right)^{2}=0$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{0}$$

Simplify.

$$x+\frac{3}{2}=0 x+\frac{3}{2}=0$$

Subtract \frac{3}{2} from both sides of the equation.

$$x=-\frac{3}{2} x=-\frac{3}{2}$$

The equation is now solved. Solutions are the same.

$$x=-\frac{3}{2}$$