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+1
238
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4x2-31x=8

aolve for x.

Feb 16, 2018

#1
+7354
+4

$$4x^2 - 31x = 8$$

Subtract  8  from both sides of the equation.

$$4x^2 - 31x - 8 = 0$$

If     $$ax^2+bx+c=0$$    then    $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

So...

If    $$4x^2 - 31x - 8 = 0$$    then    $$x = {-(-31) \pm \sqrt{(-31)^2-4(4)(-8)} \over 2(4)}$$

$$x = {-(-31) \pm \sqrt{(-31)^2-4(4)(-8)} \over 2(4)} \\~\\ x = {31 \pm \sqrt{961+128} \over 8} \\~\\ x = {31 \pm \sqrt{1089} \over 8} \\~\\ x = {31 \pm 33 \over 8} \\~\\ \begin{array} \ x=\frac{31+33}{8}\qquad&\text{or}&\qquad x=\frac{31-33}{8} \\~\\ x=\frac{64}{8}&\text{or}&\qquad x=\frac{-2}{8} \\~\\ x=8&\text{or}&\qquad x=-\frac{1}{4} \end{array}$$

.
Feb 16, 2018
edited by hectictar  Feb 16, 2018

#1
+7354
+4

$$4x^2 - 31x = 8$$

Subtract  8  from both sides of the equation.

$$4x^2 - 31x - 8 = 0$$

If     $$ax^2+bx+c=0$$    then    $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

So...

If    $$4x^2 - 31x - 8 = 0$$    then    $$x = {-(-31) \pm \sqrt{(-31)^2-4(4)(-8)} \over 2(4)}$$

$$x = {-(-31) \pm \sqrt{(-31)^2-4(4)(-8)} \over 2(4)} \\~\\ x = {31 \pm \sqrt{961+128} \over 8} \\~\\ x = {31 \pm \sqrt{1089} \over 8} \\~\\ x = {31 \pm 33 \over 8} \\~\\ \begin{array} \ x=\frac{31+33}{8}\qquad&\text{or}&\qquad x=\frac{31-33}{8} \\~\\ x=\frac{64}{8}&\text{or}&\qquad x=\frac{-2}{8} \\~\\ x=8&\text{or}&\qquad x=-\frac{1}{4} \end{array}$$

hectictar Feb 16, 2018
edited by hectictar  Feb 16, 2018
#2
+23
+2

Thank you so much. I am so grateful!!😊