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Simplifying (3x + -33)(2x + 26) = 180 Reorder the terms: (-33 + 3x)(2x + 26) = 180 Reorder the terms: (-33 + 3x)(26 + 2x) = 180 Multiply (-33 + 3x) * (26 + 2x) (-33(26 + 2x) + 3x * (26 + 2x)) = 180 ((26 * -33 + 2x * -33) + 3x * (26 + 2x)) = 180 ((-858 + -66x) + 3x * (26 + 2x)) = 180 (-858 + -66x + (26 * 3x + 2x * 3x)) = 180 (-858 + -66x + (78x + 6x2)) = 180 Combine like terms: -66x + 78x = 12x (-858 + 12x + 6x2) = 180 Solving -858 + 12x + 6x2 = 180 Solving for variable 'x'. Reorder the terms: -858 + -180 + 12x + 6x2 = 180 + -180 Combine like terms: -858 + -180 = -1038 -1038 + 12x + 6x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -1038 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-173 + 2x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-173 + 2x + x2)' equal to zero and attempt to solve: Simplifying -173 + 2x + x2 = 0 Solving -173 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '173' to each side of the equation. -173 + 2x + 173 + x2 = 0 + 173 Reorder the terms: -173 + 173 + 2x + x2 = 0 + 173 Combine like terms: -173 + 173 = 0 0 + 2x + x2 = 0 + 173 2x + x2 = 0 + 173 Combine like terms: 0 + 173 = 173 2x + x2 = 173 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 = 173 + 1 Reorder the terms: 1 + 2x + x2 = 173 + 1 Combine like terms: 173 + 1 = 174 1 + 2x + x2 = 174 Factor a perfect square on the left side: (x + 1)(x + 1) = 174 Calculate the square root of the right side: 13.190905958 Break this problem into two subproblems by setting (x + 1) equal to 13.190905958 and -13.190905958.Subproblem 1
x + 1 = 13.190905958 Simplifying x + 1 = 13.190905958 Reorder the terms: 1 + x = 13.190905958 Solving 1 + x = 13.190905958 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 = 13.190905958 + -1 Combine like terms: 1 + -1 = 0 0 + x = 13.190905958 + -1 x = 13.190905958 + -1 Combine like terms: 13.190905958 + -1 = 12.190905958 x = 12.190905958 Simplifying x = 12.190905958Subproblem 2
x + 1 = -13.190905958 Simplifying x + 1 = -13.190905958 Reorder the terms: 1 + x = -13.190905958 Solving 1 + x = -13.190905958 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 = -13.190905958 + -1 Combine like terms: 1 + -1 = 0 0 + x = -13.190905958 + -1 x = -13.190905958 + -1 Combine like terms: -13.190905958 + -1 = -14.190905958 x = -14.190905958 Simplifying x = -14.190905958Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.190905958, -14.190905958}Solution
x = {12.190905958, -14.190905958}
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