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McGraw Hill Integrated II, 2012 View details

5. Solving Quadratic Equations by Using the Quadratic Formula

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Exercise 29 Page 137

Make sure you write all the terms on the left-hand side of the equation and simplify as much as possible before using the Quadratic Formula.

- 1.2, 5.2

Practice makes perfect

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 - 8x = 12

SubEqn

LHS-12=RHS-12

2x^2 - 8x - 12 = 0

FactorOut

Factor out 2

2(x^2 - 4x - 6) = 0

DivEqn

.LHS /2.=.RHS /2.

x^2 - 4x - 6 = 0

Now, we can identify the values of a, b, and c. x^2 - 4x - 6 ⇕ 1x^2+( - 4)x+( - 6)=0 We see that a= 1, b= - 4, and c= - 6. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( - 4)±sqrt(( - 4)^2-4( 1)( - 6))/2( 1)

▼

Solve for x and Simplify

NegNeg

- (- a)=a

x=4±sqrt((- 4)^2-4(1)(- 6))/2(1)

CalcPow

Calculate power

x=4±sqrt(16-4(1)(- 6))/2(1)