Precalculus Examples

$1.8 = a x^{2} + b x + c$

Step 1

Rewrite the equation as $a x^{2} + b x + c = 1.8$ .

$a x^{2} + b x + c = 1.8$

Step 2

Subtract $1.8$ from both sides of the equation.

$a x^{2} + b x + c - 1.8 = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = a$ , $b = b$ , and $c = c - 1.8$ into the quadratic formula and solve for $x$ .

$\frac{- b \pm \sqrt{b^{2} - 4 \cdot (a \cdot (c - 1.8))}}{2 a}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c - 4 a \cdot - 1.8}}{2 a}$

Step 5.2

Multiply $- 1.8$ by $- 4$ .

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c + 7.2 a}}{2 a}$

Step 6

The final answer is the combination of both solutions.

$x = - \frac{b - \sqrt{b^{2} - 4 a c + 7.2 a}}{2 a}$

$x = - \frac{b + \sqrt{b^{2} - 4 a c + 7.2 a}}{2 a}$