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Simplifying 4x2 + 12x + -138 = 0 Reorder the terms: -138 + 12x + 4x2 = 0 Solving -138 + 12x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-69 + 6x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-69 + 6x + 2x2)' equal to zero and attempt to solve: Simplifying -69 + 6x + 2x2 = 0 Solving -69 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -34.5 + 3x + x2 = 0 Move the constant term to the right: Add '34.5' to each side of the equation. -34.5 + 3x + 34.5 + x2 = 0 + 34.5 Reorder the terms: -34.5 + 34.5 + 3x + x2 = 0 + 34.5 Combine like terms: -34.5 + 34.5 = 0.0 0.0 + 3x + x2 = 0 + 34.5 3x + x2 = 0 + 34.5 Combine like terms: 0 + 34.5 = 34.5 3x + x2 = 34.5 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 = 34.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 34.5 + 2.25 Combine like terms: 34.5 + 2.25 = 36.75 2.25 + 3x + x2 = 36.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 36.75 Calculate the square root of the right side: 6.062177826 Break this problem into two subproblems by setting (x + 1.5) equal to 6.062177826 and -6.062177826.Subproblem 1
x + 1.5 = 6.062177826 Simplifying x + 1.5 = 6.062177826 Reorder the terms: 1.5 + x = 6.062177826 Solving 1.5 + x = 6.062177826 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 = 6.062177826 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.062177826 + -1.5 x = 6.062177826 + -1.5 Combine like terms: 6.062177826 + -1.5 = 4.562177826 x = 4.562177826 Simplifying x = 4.562177826Subproblem 2
x + 1.5 = -6.062177826 Simplifying x + 1.5 = -6.062177826 Reorder the terms: 1.5 + x = -6.062177826 Solving 1.5 + x = -6.062177826 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 = -6.062177826 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.062177826 + -1.5 x = -6.062177826 + -1.5 Combine like terms: -6.062177826 + -1.5 = -7.562177826 x = -7.562177826 Simplifying x = -7.562177826Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.562177826, -7.562177826}Solution
x = {4.562177826, -7.562177826}
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