Question

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. 5y2 − 8y = 2

Answer 1

5y2-8y=2
(Given equation)
10y-8y=2
(Simplifying [5y2] to 10 y)
2y=2
(simplifing [10y-8y] to 2 y)
y=1
(Dividing by 2 on both sides of the equal sign leaving us with the answer of y=2)

Answer 2

The solution of 5y² − 8y = 2 is 1.82 or − 0.22

Further explanation

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

D = b² - 4 a c

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

An axis of symmetry of quadratic equation y = ax² + bx + c is :

$\large {\boxed {x = \frac{-b}{2a} } }$

Let us now tackle the problem!

Given:

$5y^2 - 8y = 2$

$5y^2 - 8y - 2 = 0$

$\text{Let} : a = 5 , b = - 8 , c = -2$

We will use the quadratic formula to solve the equation.

$y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$y = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(5)(-2)}}{2(5)}$

$y = \frac{8 \pm \sqrt{64 +40}}{10}$

$y = \frac{8 \pm \sqrt{104}}{10}$

$y_1 = \frac{8 + \sqrt{104}}{10} ~\text{or} ~ y_2 = \frac{8 - \sqrt{104}}{10}$

$\boxed {y_1 = 1.82} ~ \text{or} ~ \boxed {y_2 = -0.22}$

Learn more

• Solving Quadratic Equations by Factoring : https://brainly.com/question/12182022
• Determine the Discriminant : https://brainly.com/question/4600943
• Formula of Quadratic Equations : https://brainly.com/question/3776858

Answer details

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number