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