How do you use the quadratic formula to solve 4.8x^2=5.2x+2.7?

Jun 28, 2017

See a solution process below:

Explanation:

First, move each term to the left side of the equation to equate it to $0$ while keeping the equation balanced:

$4.8 {x}^{2} - \textcolor{red}{5.2 x} - \textcolor{b l u e}{2.7} = 5.2 x - \textcolor{red}{5.2 x} + 2.7 - \textcolor{b l u e}{2.7}$

$4.8 {x}^{2} - 5.2 x - 2.7 = 0 + 0$

$4.8 {x}^{2} - 5.2 x - 2.7 = 0$

For $a {x}^{2} + b x + c = 0$, the values of $x$ which are the solutions to the equation are given by:

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

Substituting $4.8$ for $a$; $- 5.2$ for $b$ and $- 2.7$ for $c$ gives:

$x = \frac{- \left(- 5.2\right) \pm \sqrt{{\left(- 5.2\right)}^{2} - \left(4 \cdot 4.8 \cdot - 2.7\right)}}{2 \cdot 4.8}$

$x = \frac{5.2 \pm \sqrt{27.04 - \left(- 51.84\right)}}{9.6}$

$x = \frac{5.2 \pm \sqrt{27.04 + 51.84}}{9.6}$

$x = \frac{5.2 \pm \sqrt{78.88}}{9.6}$

$x = \frac{5.2 + \sqrt{78.88}}{9.6}$ and $x = \frac{5.2 - \sqrt{78.88}}{9.6}$

$x = \frac{5.2 + 8.88}{9.6}$ and $x = \frac{5.2 - 8.88}{9.6}$

$x = \frac{14.08}{9.6}$ and $x = - \frac{3.68}{9.6}$

$x = 1.47$ and $x = - 0.38$

Rounded to the nearest hundredth.

Jun 28, 2017

$x \approx 1.47$ and $x \approx - 0.38$

Explanation:

A quadratic equation is in the from $a {x}^{2} + b x + c = 0$ where a,b, and c are the numerical coefficients of the unknown variable $x$.

First subtract $- 4.8 {x}^{2}$ from both sides of the equation to get one side equal to $0$.

The quadratic formula: $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
Just insert the respective coefficients into the formula to get

$x = \frac{- 5.2 \pm \sqrt{27.04 - 4 \left(- 4.8\right) 2.7}}{- 9.6}$

Find the value of the square root:
$x = \frac{- 5.2 \pm \sqrt{78.88}}{- 9.6}$ then $x \approx \frac{- 5.2 \pm 8.88}{- 9.6}$

Solve the fraction separately, once using addition and once subtraction:
$x \approx \frac{- 5.2 + 8.88}{- 9.6}$ then $x \approx - \frac{3.68}{9.6}$

$x \approx \frac{- 5.2 - 8.88}{- 9.6}$ then $x \approx - \frac{14.08}{-} 9.6$