Exercise 56 Page 767

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 We first need to identify the values of a, b, and c. x^2+12x+36=0 ⇕ 1x^2+ 12x+ 36=0 We see that a= 1, b= 12, and c= 36. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 12±sqrt(( 12)^2-4( 1)( 36))/2( 1)

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Solve for x and Simplify

CalcPow

Calculate power

x=- 12±sqrt(144-4(1)(36))/2(1)

Multiply

Multiply

x=- 12±sqrt(144-144)/2

SubTerms

Subtract terms

x=- 12±sqrt(0)/2

CalcRoot

Calculate root

- 12± 0/2

Since adding or subtracting zero does not change the value of a number, the numerator will simplify to - 12. Therefore, we will get only one value of x. x= - 12/2 ⇔ x= - 6 Using the Quadratic Formula, we found that the solution of the given equation is x=- 6.