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Simplifying (6x2) + (12x) + -8 = 0 Reorder the terms: -8 + (12x) + (6x2) = 0 Solving -8 + (12x) + (6x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + (6x) + (3x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + (6x) + (3x2))' equal to zero and attempt to solve: Simplifying -4 + (6x) + (3x2) = 0 Solving -4 + (6x) + (3x2) = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + (2x) + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + (2x) + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + (2x) + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + (2x) + x2 = 0 + 1.333333333 (2x) + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 (2x) + x2 = 1.333333333 The x term is (2x). Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. (2x) + 1 + x2 = 1.333333333 + 1 Reorder the terms: 1 + (2x) + x2 = 1.333333333 + 1 Combine like terms: 1.333333333 + 1 = 2.333333333 1 + (2x) + x2 = 2.333333333 Factor a perfect square on the left side: ((x) + 1)((x) + 1) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting ((x) + 1) equal to 1.527525232 and -1.527525232.Subproblem 1
(x) + 1 = 1.527525232 Simplifying (x) + 1 = 1.527525232 x + 1 = 1.527525232 Reorder the terms: 1 + x = 1.527525232 Solving 1 + x = 1.527525232 Solving for variable 'x'. 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 = 1.527525232 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.527525232 + -1 x = 1.527525232 + -1 Combine like terms: 1.527525232 + -1 = 0.527525232 x = 0.527525232 Simplifying x = 0.527525232Subproblem 2
(x) + 1 = -1.527525232 Simplifying (x) + 1 = -1.527525232 x + 1 = -1.527525232 Reorder the terms: 1 + x = -1.527525232 Solving 1 + x = -1.527525232 Solving for variable 'x'. 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 = -1.527525232 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.527525232 + -1 x = -1.527525232 + -1 Combine like terms: -1.527525232 + -1 = -2.527525232 x = -2.527525232 Simplifying x = -2.527525232Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.527525232, -2.527525232}Solution
x = {0.527525232, -2.527525232}
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