Part 1) x=3

Part 2) x = −1.11 and x = 1.11

Part 3) 105

Part 4) a = −6, b = 9, c = −7

Part 5) x equals 5 plus or minus the square root of 33, all over 2

Part 6) In the procedure

Part 7)

Part 8) The denominator is 2

Part 9) a = −6, b = −8, c = 12

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form is equal to

Part 1)

in this problem we have

so

substitute in the formula

Part 2) in this problem we have

so

substitute in the formula

Part 3) When the solution of x2 − 9x − 6 is expressed as 9 plus or minus the square root of r, all over 2, what is the value of r?

in this problem we have

so

substitute in the formula

therefore

Part 4) What are the values a, b, and c in the following quadratic equation?

−6x2 = −9x + 7

in this problem we have

so

Part 5) Use the quadratic formula to find the exact solutions of x2 − 5x − 2 = 0.

In this problem we have

so

substitute in the formula

therefore

x equals 5 plus or minus the square root of 33, all over 2

Part 6) Quadratic Formula proof

we have

Divide both sides by a

Complete the square

Rewrite the perfect square trinomial on the left side of the equation as a binomial squared

Find a common denominator on the right side of the equation

Take the square root of both sides of the equation

Simplify the right side of the equation

Subtract the quantity b over 2 times a from both sides of the equation

Part 7) in this problem we have

so

substitute in the formula

therefore

The other solution is

Part 8) in this problem we have

so

substitute in the formula

therefore

The denominator is 2

Part 9) What are the values a, b, and c in the following quadratic equation?

−6x2 − 8x + 12

in this problem we have

so