Exercise 42 Page 145

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.

2x^2+6x=7

SubEqn

LHS-7=RHS-7

2x^2+6x-7=0

Now, we can identify the values of a, b, and c. 2x^2+6x-7=0 ⇕ 2x^2+ 6x+( - 7)=0 We see that a= 2, b= 6, and c= - 7. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 6±sqrt(6^2-4( 2)( - 7))/2( 2)

▼

Solve for x and Simplify

CalcPow

Calculate power

x=-6±sqrt(36-4(2)(- 7))/2(2)

Multiply

Multiply

x=-6±sqrt(36-8(- 7))/4

MultNegNegOnePar

- a(- b)=a* b

x=-6±sqrt(36+56)/4

AddTerms

Add terms

x=-6±sqrt(92)/4

SplitIntoFactors

Split into factors

x=-6±sqrt(4* 23)/4

SqrtProd

sqrt(a* b)=sqrt(a)*sqrt(b)

x=-6± sqrt(4)* sqrt(23)/4

CalcRoot

Calculate root

x=-6± 2 sqrt(23)/4

FactorOut

Factor out 2

x=2(-3± sqrt(23))/4

CancelCommonFac

Cancel out common factors

x=-3± sqrt(23)/2

Using the Quadratic Formula, we found that the solutions of the given equation are x= -3± sqrt(23)2. Let's use a calculator to approximate our solutions. We see that rounded solutions are x_1= -3+sqrt(23)2≈ 0.9 and x_2= -3-sqrt(23)2≈ -3.9.