"Solve the quadratic equation using the quadratic formula...." solved and explained

High School
Algebra
Algebra I
Quadratic function and equation

Braxton Pugh

Answered question

2021-02-21

Solve the quadratic equation using the quadratic formula.

2 x^{2} - 6 x + 5 = 0

Answer & Explanation

Fatema Sutton

Skilled2021-02-22Added 88 answers

Given quadratic equation is $2 x^{2} - 6 x + 5 = 0 .$
Standard equation of quadratic equation is $a x^{2} + b x + c = 0$ .
On comparing the given equation with standard equation of quadratic equation, we get a=2, b=−6 and c=5
Quadratic formula is given as:
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2} a$
Therefore, solving given quadratic equation with quadratic formula,
$x = \frac{- (- 6) \pm \sqrt{{(- 6)}^{2} - 4 (2) (5)}}{2} (2)$
$= \frac{6 \pm \sqrt{36 - 40}}{4}$
$= \frac{6 \pm \sqrt{-} 4}{4}$
$= (6 \pm \frac{\sqrt{4 i}}{4} (\sqrt{-} 1 = i))$
$= \frac{6 \pm 2 i}{4}$
$= \frac{3 \pm i}{2}$
Therefore, required solution of given quadratic equation is: x=(3+i)/2 or x=(3-i)/2

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