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Simplifying (8x + -1)(3x + -6) = 180 Reorder the terms: (-1 + 8x)(3x + -6) = 180 Reorder the terms: (-1 + 8x)(-6 + 3x) = 180 Multiply (-1 + 8x) * (-6 + 3x) (-1(-6 + 3x) + 8x * (-6 + 3x)) = 180 ((-6 * -1 + 3x * -1) + 8x * (-6 + 3x)) = 180 ((6 + -3x) + 8x * (-6 + 3x)) = 180 (6 + -3x + (-6 * 8x + 3x * 8x)) = 180 (6 + -3x + (-48x + 24x2)) = 180 Combine like terms: -3x + -48x = -51x (6 + -51x + 24x2) = 180 Solving 6 + -51x + 24x2 = 180 Solving for variable 'x'. Reorder the terms: 6 + -180 + -51x + 24x2 = 180 + -180 Combine like terms: 6 + -180 = -174 -174 + -51x + 24x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -174 + -51x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-58 + -17x + 8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-58 + -17x + 8x2)' equal to zero and attempt to solve: Simplifying -58 + -17x + 8x2 = 0 Solving -58 + -17x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -7.25 + -2.125x + x2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -2.125x + 7.25 + x2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -2.125x + x2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -2.125x + x2 = 0 + 7.25 -2.125x + x2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -2.125x + x2 = 7.25 The x term is -2.125x. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125x + 1.12890625 + x2 = 7.25 + 1.12890625 Reorder the terms: 1.12890625 + -2.125x + x2 = 7.25 + 1.12890625 Combine like terms: 7.25 + 1.12890625 = 8.37890625 1.12890625 + -2.125x + x2 = 8.37890625 Factor a perfect square on the left side: (x + -1.0625)(x + -1.0625) = 8.37890625 Calculate the square root of the right side: 2.894634044 Break this problem into two subproblems by setting (x + -1.0625) equal to 2.894634044 and -2.894634044.Subproblem 1
x + -1.0625 = 2.894634044 Simplifying x + -1.0625 = 2.894634044 Reorder the terms: -1.0625 + x = 2.894634044 Solving -1.0625 + x = 2.894634044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = 2.894634044 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = 2.894634044 + 1.0625 x = 2.894634044 + 1.0625 Combine like terms: 2.894634044 + 1.0625 = 3.957134044 x = 3.957134044 Simplifying x = 3.957134044Subproblem 2
x + -1.0625 = -2.894634044 Simplifying x + -1.0625 = -2.894634044 Reorder the terms: -1.0625 + x = -2.894634044 Solving -1.0625 + x = -2.894634044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = -2.894634044 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = -2.894634044 + 1.0625 x = -2.894634044 + 1.0625 Combine like terms: -2.894634044 + 1.0625 = -1.832134044 x = -1.832134044 Simplifying x = -1.832134044Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.957134044, -1.832134044}Solution
x = {3.957134044, -1.832134044}
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