Exercise 46 Page 138

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. - 2x^2 - 7x = - 1.5 ⇕ - 2x^2 - 7x + 1.5 = 0 Now, we can identify the values of a, b, and c. - 2x^2 - 7x + 1.5 = 0 ⇕ - 2x^2+( - 7)x+ 1.5=0 We see that a= - 2, b= - 7, and c= 1.5. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( -7)±sqrt(( - 7)^2-4( -2)( 1.5))/2( - 2)

▼

Solve for x and Simplify

NegNeg

- (- a)=a

x=7±sqrt((- 7)^2-4(-2)(1.5))/2(- 2)

CalcPow

Calculate power

x=7±sqrt(49-4(-2)(1.5))/2(- 2)

MultNegNegOnePar

- a(- b)=a* b

x=7±sqrt(49+8(1.5))/2(- 2)

Multiply

Multiply

x=7±sqrt(49+12)/- 4

AddTerms

Add terms

x=7±sqrt(61)/- 4

MoveNegDenomToFrac

Put minus sign in front of fraction

x=- 7± sqrt(61)/4

The solutions for this equation are x=- 7± sqrt(61)4. Let's separate them into the positive and negative cases.

x=- 7± sqrt(61)/4
x=- 7 + sqrt(61)/4	x_2=x=- 7 - sqrt(61)4
x_1≈ - 3.7	x_2 ≈ 0.2

Using the Quadratic Formula, we found that the solutions of the given equation are x_1 ≈ - 3.7 and x_2 ≈ 0.2.