Exercise 20 Page 137

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 - 5x = - 7 ⇔ 2x^2 - 5x + 7 = 0 Now, we can identify the values of a, b, and c. 2x^2 - 5x + 7 = 0 ⇕ 2x^2+( - 5)x+ 7=0 We see that a= 2, b= - 5, and c= 7. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( -5)±sqrt(( - 5)^2-4( 2)( 7))/2( 2)

NegNeg

- (- a)=a

x=5±sqrt((- 5)^2-4(2)(7))/2(2)

CalcPow

Calculate power

x=5±sqrt(25-4(2)(7))/2(2)

Multiply

Multiply

x=5±sqrt(25-56)/4

SubTerm

Subtract term

x=5±sqrt(- 31)/4

Since we cannot calculate the root of a negative number, there are no real solutions of the given equation.