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Simplifying 9x2 + 18x + -12 = 0 Reorder the terms: -12 + 18x + 9x2 = 0 Solving -12 + 18x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 6x + 3x2) = 0 Ignore the factor 3.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 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 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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