solve the quadratic equation 4x²+ 12x+8 =0
Answers
Answer:
4x²+ 12x+8 =0
(22x2 - 12x) + 8 = 0
4x2 - 12x + 8 = 4 • (x2 - 3x + 2)
Factoring x2 - 3x + 2
The first term is, x2 its coefficient is 1 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is +2
Step-1 : Multiply the coefficient of the first term by the constant 1 • 2 = 2
Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is -3 .
Answer:
Reorder the terms:
8 + 12x + 4x2 = 0
Solving
8 + 12x + 4x2 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 3x + x2) = 0
Factor a trinomial.
4((2 + x)(1 + x)) = 0
Ignore the factor 4.
Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:
Simplifying
2 + x = 0
Solving
2 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2
Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2
Combine like terms: 0 + -2 = -2
x = -2
Simplifying
x = -2
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:
Simplifying
1 + x = 0
Solving
1 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1
Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1
Combine like terms: 0 + -1 = -1
x = -1
Simplifying
x = -1
Solution
x = {-2, -1}