Exercise 42 Page 160

We will use the Quadratic Formula to solve the given quadratic equation. ax^2+ bx+ c=0 ⇕ x=- b± sqrt(b^2-4 a c)/2 a Let's start by rewriting the equation so all of the terms are on the left-hand side and then simplify as much as possible.

2h^2+8h+3=3

SubEqn

LHS-3=RHS-3

2h^2+8h=0

Now, we can identify the values of a, b, and c. 2h^2+8h=0 ⇕ 2h^2+ 8h+ 0=0 We see that a= 2, b= 8, and c= 0. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 8±sqrt(8^2-4( 2)( 0))/2( 2)

▼

Solve for x and Simplify

CalcPow

Calculate power

x=-8±sqrt(64-4(2)(0))/2(2)

Multiply

Multiply

x=-8±sqrt(64-8(0))/4

ZeroPropMult

Zero Property of Multiplication

x=-8±sqrt(64-0)/4

SubTerm

Subtract term

x=-8±sqrt(64)/4

CalcRoot

Calculate root

x=-8±8/4

The solutions for this equation are x= -8±84. Let's separate them into positive and negative cases.

x=-8±8/4
x_1=-8+8/4	x_2=-8-8/4
x_1=0/4	x_2=-16/4
x_1=0	x_2=-4

Using the Quadratic Formula, we found that the solutions of the given equation are x_1=0 and x_2=-4.