# How do you use the quadratic formula to solve 1/4x^2+5x-4=0?

Jun 5, 2018

$x = - 10 \pm 2 \sqrt{29}$

#### Explanation:

Multiplying by $4$ we get
${x}^{2} + 20 x - 16 = 0$
so we have
${x}_{1 , 2} = - 10 \pm 2 \setminus \sqrt{29}$

Jun 5, 2018

$x = 0.770 \mathmr{and} x = - 20.77$

#### Explanation:

You can multiply each term in the equation by $4$ to get rid of the fraction. This does not change the equation or the solutions.

$\frac{1}{4} {x}^{2} + 5 x - 4 = 0$

$\textcolor{b l u e}{4} \times \frac{1}{4} {x}^{2} + \textcolor{b l u e}{4} \times 5 x - \textcolor{b l u e}{4} \times 4 = \textcolor{b l u e}{4} \times 0$

${x}^{2} + 20 x - 16 = 0$

This is now in the form $a {x}^{2} + b x + c = 0$

$a = 1 , b = 20 \mathmr{and} c = - 16$

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

$x = \frac{- \left(20\right) \pm \sqrt{{\left(20\right)}^{2} - 4 \left(1\right) \left(- 16\right)}}{2 \left(1\right)}$

$x = \frac{- 20 \pm \sqrt{400 + 64}}{2}$

$x = \frac{- 20 \pm \sqrt{464}}{2}$

$x = 0.770 \mathmr{and} x = - 20.77$

Jun 5, 2018

$x = - 10 \pm 2 \sqrt{29}$

#### Explanation:

$\frac{1}{4} {x}^{2} + 5 x - 4 = 0$

First let's get rid of the fraction, we can put a fraction in the quadratic formula but it is easier not to:

$4 \left(\frac{1}{4} {x}^{2} + 5 x - 4 = 0\right)$

${x}^{2} + 20 x - 16 = 0$

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

a = 1

b= 20

c=-16

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

$x = \frac{- 20 \pm \sqrt{{20}^{2} - 4 \cdot 1 \cdot \left(- 16\right)}}{2 \cdot 1}$

$x = \frac{- 20 \pm \sqrt{400 + 64}}{2}$

$x = \frac{- 20 \pm 4 \sqrt{29}}{2}$

$x = - 10 \pm 2 \sqrt{29}$