Skip to main content
Solve for x
Tick mark Image
Graph

Similar Problems from Web Search

Share

x^{2}+2x-0.44=0
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=\frac{-2±\sqrt{2^{2}-4\left(-0.44\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -0.44 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-2±\sqrt{4-4\left(-0.44\right)}}{2}
Square 2.
x=\frac{-2±\sqrt{4+1.76}}{2}
Multiply -4 times -0.44.
x=\frac{-2±\sqrt{5.76}}{2}
Add 4 to 1.76.
x=\frac{-2±\frac{12}{5}}{2}
Take the square root of 5.76.
x=\frac{\frac{2}{5}}{2}
Now solve the equation x=\frac{-2±\frac{12}{5}}{2} when ± is plus. Add -2 to \frac{12}{5}.
x=\frac{1}{5}
Divide \frac{2}{5} by 2.
x=-\frac{\frac{22}{5}}{2}
Now solve the equation x=\frac{-2±\frac{12}{5}}{2} when ± is minus. Subtract \frac{12}{5} from -2.
x=-\frac{11}{5}
Divide -\frac{22}{5} by 2.
x=\frac{1}{5} x=-\frac{11}{5}
The equation is now solved.
x^{2}+2x-0.44=0
Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.
x^{2}+2x-0.44-\left(-0.44\right)=-\left(-0.44\right)
Add 0.44 to both sides of the equation.
x^{2}+2x=-\left(-0.44\right)
Subtracting -0.44 from itself leaves 0.
x^{2}+2x=0.44
Subtract -0.44 from 0.
x^{2}+2x+1^{2}=0.44+1^{2}
Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+2x+1=0.44+1
Square 1.
x^{2}+2x+1=1.44
Add 0.44 to 1.
\left(x+1\right)^{2}=1.44
Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x+1\right)^{2}}=\sqrt{1.44}
Take the square root of both sides of the equation.
x+1=\frac{6}{5} x+1=-\frac{6}{5}
Simplify.
x=\frac{1}{5} x=-\frac{11}{5}
Subtract 1 from both sides of the equation.