Question

Directions: Using the quadratic formula follow theprocedure in solving quadratic equation 2x2 - 2x = x + 3 1. Write the equation in standard form (zero on one side of the equation) 2. List the numerical values of the coefficients a, b, and c. 3. Write the quadratic formula. 4. Substitute the numerical values for a, b, and c in the quadratic formula 5. Simplify to get the exact solutions. 6. Use a calculator if necessary.

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Answer 1

Step-by-step explanation:

$\tt We \: have,$

$\tt 2x^2-2x=x+31$

$\tt 2x^2-2x-x-31=0$

$\tt 2x^2-3x-31=0$

$\tt Standard \:form \:of\: a\: quadratic \:equation :$

$\tt ax^2+bx+c=0$

$\tt coefficients:$

• a= 2
• b= -3
• c= -31

$\tt Quadratic \: formula:$

$\tt x= \dfrac{-b±\sqrt{b^2-4ac}}{2a}$

$\tt x=\dfrac{-(-3)±\sqrt{(-3)^2-4(2)(-31)}}{2(2)}$

$\tt =\dfrac{3±\sqrt{9+248}}{4}\tt$

$\tt =\dfrac{3±\sqrt{257}}{4}$

The solutions of the quadratic equation:

$\tt x =\dfrac{3+\sqrt{257}}{4}\:or\:x=\dfrac{3-\sqrt{257}}{4}$