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Simplifying (3x + -33)(2x + 26) = 360 Reorder the terms: (-33 + 3x)(2x + 26) = 360 Reorder the terms: (-33 + 3x)(26 + 2x) = 360 Multiply (-33 + 3x) * (26 + 2x) (-33(26 + 2x) + 3x * (26 + 2x)) = 360 ((26 * -33 + 2x * -33) + 3x * (26 + 2x)) = 360 ((-858 + -66x) + 3x * (26 + 2x)) = 360 (-858 + -66x + (26 * 3x + 2x * 3x)) = 360 (-858 + -66x + (78x + 6x2)) = 360 Combine like terms: -66x + 78x = 12x (-858 + 12x + 6x2) = 360 Solving -858 + 12x + 6x2 = 360 Solving for variable 'x'. Reorder the terms: -858 + -360 + 12x + 6x2 = 360 + -360 Combine like terms: -858 + -360 = -1218 -1218 + 12x + 6x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -1218 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-203 + 2x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-203 + 2x + x2)' equal to zero and attempt to solve: Simplifying -203 + 2x + x2 = 0 Solving -203 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '203' to each side of the equation. -203 + 2x + 203 + x2 = 0 + 203 Reorder the terms: -203 + 203 + 2x + x2 = 0 + 203 Combine like terms: -203 + 203 = 0 0 + 2x + x2 = 0 + 203 2x + x2 = 0 + 203 Combine like terms: 0 + 203 = 203 2x + x2 = 203 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 = 203 + 1 Reorder the terms: 1 + 2x + x2 = 203 + 1 Combine like terms: 203 + 1 = 204 1 + 2x + x2 = 204 Factor a perfect square on the left side: (x + 1)(x + 1) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (x + 1) equal to 14.282856857 and -14.282856857.Subproblem 1
x + 1 = 14.282856857 Simplifying x + 1 = 14.282856857 Reorder the terms: 1 + x = 14.282856857 Solving 1 + x = 14.282856857 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 = 14.282856857 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.282856857 + -1 x = 14.282856857 + -1 Combine like terms: 14.282856857 + -1 = 13.282856857 x = 13.282856857 Simplifying x = 13.282856857Subproblem 2
x + 1 = -14.282856857 Simplifying x + 1 = -14.282856857 Reorder the terms: 1 + x = -14.282856857 Solving 1 + x = -14.282856857 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 = -14.282856857 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.282856857 + -1 x = -14.282856857 + -1 Combine like terms: -14.282856857 + -1 = -15.282856857 x = -15.282856857 Simplifying x = -15.282856857Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.282856857, -15.282856857}Solution
x = {13.282856857, -15.282856857}
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