Lennie Carroll

2021-02-09

Solution to quadratic equation Quadratic formula -2 Examples with solution and checking

### Answer & Explanation

Velsenw

The quadratic formula for an equation
Consider the quadratic equation ${x}^{2}+5x+6=0.$
Compare the equation with standard form $a{x}^{2}+bx+c=0.$
Here,
Evaluate the solutions of the quadratic equation as follows.
$x=\frac{-5±\sqrt{{5}^{2}-4\left(1\right)\left(6\right)}}{2}\left(1\right)$
$x=\frac{-5±\sqrt{25-24}}{2}$
$x=\frac{5±1}{2}$
$x=\frac{-5+1}{2}\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}x=\frac{-5-1}{2}$

Verification:
Substitute $x=-2$ in the quadratic equation and verify the solution as follows.
${\left(-2\right)}^{2}+5\left(-2\right)+6=0$
$4-10+6=0$
$0=0$ (True)
Thus, the solution $x=-2$ is verified.
Substitute $x=-3$ in the quadratic equation and verify the solution as follows.
${\left(-3\right)}^{2}+5\left(-3\right)+6=0$
$9-15+6=0$
$0=0$ (True)
Thus, the solution $x=-3$ is verified.

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