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Simplifying (18x2 + -6x2) + (36x + -12) = 0 Combine like terms: 18x2 + -6x2 = 12x2 (12x2) + (36x + -12) = 0 (12x2) + (36x + -12) = 0 Reorder the terms: (12x2) + (-12 + 36x) = 0 Remove parenthesis around (-12 + 36x) (12x2) + -12 + 36x = 0 Reorder the terms: -12 + 36x + (12x2) = 0 Solving -12 + 36x + (12x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-1 + 3x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-1 + 3x + x2)' equal to zero and attempt to solve: Simplifying -1 + 3x + x2 = 0 Solving -1 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 3x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 3x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3x + x2 = 0 + 1 3x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 3x + x2 = 1 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 1 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1 + 2.25 Combine like terms: 1 + 2.25 = 3.25 2.25 + 3x + x2 = 3.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 1.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 1.5 = 1.802775638 Simplifying x + 1.5 = 1.802775638 Reorder the terms: 1.5 + x = 1.802775638 Solving 1.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.802775638 + -1.5 x = 1.802775638 + -1.5 Combine like terms: 1.802775638 + -1.5 = 0.302775638 x = 0.302775638 Simplifying x = 0.302775638Subproblem 2
x + 1.5 = -1.802775638 Simplifying x + 1.5 = -1.802775638 Reorder the terms: 1.5 + x = -1.802775638 Solving 1.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.802775638 + -1.5 x = -1.802775638 + -1.5 Combine like terms: -1.802775638 + -1.5 = -3.302775638 x = -3.302775638 Simplifying x = -3.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.302775638, -3.302775638}Solution
x = {0.302775638, -3.302775638}
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