6x²+3x+24=0
by quadrabic formula
Answers
Answer:
Simplifying
6x2 + -3x + -24 = 0
Reorder the terms:
-24 + -3x + 6x2 = 0
Solving
-24 + -3x + 6x2 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -1x + 2x2) = 0
Ignore the factor 3.
Subproblem 1
Set the factor '(-8 + -1x + 2x2)' equal to zero and attempt to solve:
Simplifying
-8 + -1x + 2x2 = 0
Solving
-8 + -1x + 2x2 = 0
Begin completing the square. Divide all terms by
2 the coefficient of the squared term:
Divide each side by '2'.
-4 + -0.5x + x2 = 0
Move the constant term to the right:
Add '4' to each side of the equation.
-4 + -0.5x + 4 + x2 = 0 + 4
Reorder the terms:
-4 + 4 + -0.5x + x2 = 0 + 4
Combine like terms: -4 + 4 = 0
0 + -0.5x + x2 = 0 + 4
-0.5x + x2 = 0 + 4
Combine like terms: 0 + 4 = 4
-0.5x + x2 = 4
The x term is -0.5x. Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.
Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 4 + 0.0625
Reorder the terms:
0.0625 + -0.5x + x2 = 4 + 0.0625
Combine like terms: 4 + 0.0625 = 4.0625
0.0625 + -0.5x + x2 = 4.0625
Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 4.0625
Calculate the square root of the right side: 2.015564437
Break this problem into two subproblems by setting
(x + -0.25) equal to 2.015564437 and -2.015564437.
Subproblem 1
x + -0.25 = 2.015564437
Simplifying
x + -0.25 = 2.015564437
Reorder the terms:
-0.25 + x = 2.015564437
Solving
-0.25 + x = 2.015564437
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 2.015564437 + 0.25
Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 2.015564437 + 0.25
x = 2.015564437 + 0.25
Combine like terms: 2.015564437 + 0.25 = 2.265564437
x = 2.265564437
Simplifying
x = 2.265564437
Subproblem 2
x + -0.25 = -2.015564437
Simplifying
x + -0.25 = -2.015564437
Reorder the terms:
-0.25 + x = -2.015564437
Solving
-0.25 + x = -2.015564437
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -2.015564437 + 0.25
Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -2.015564437 + 0.25
x = -2.015564437 + 0.25
Combine like terms: -2.015564437 + 0.25 = -1.765564437
x = -1.765564437
Simplifying
x = -1.765564437
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.265564437, -1.765564437}
Solution
x = {2.265564437, -1.765564437}