To solve a quadratic equation means to find the values of the variable (usually xxx) that make the equation true. A quadratic equation is any equation that can be written in the form:
ax2+bx+c=0ax^2+bx+c=0ax2+bx+c=0
where aaa, bbb, and ccc are constants and a≠0a\neq 0a=0.
What does "solving" mean here?
- It means finding the roots or solutions of the equation.
- These solutions are the values of xxx that satisfy the equation - when you substitute them back into the equation, the left side equals zero.
- There can be two solutions , one solution , or no real solutions depending on the equation.
How do you solve a quadratic equation?
Common methods include:
- Factoring (if possible)
- Using the quadratic formula:
x=−b±b2−4ac2ax=\frac{-b\pm \sqrt{b^2-4ac}}{2a}x=2a−b±b2−4ac
- Completing the square
- Graphing (finding where the parabola crosses the x-axis)
Summary
Solving a quadratic equation means finding the value(s) of xxx that satisfy the equation ax2+bx+c=0ax^2+bx+c=0ax2+bx+c=0. These values are called the roots or solutions of the quadratic.
