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Simplifying 3x(5x + -6) = 180 Reorder the terms: 3x(-6 + 5x) = 180 (-6 * 3x + 5x * 3x) = 180 (-18x + 15x2) = 180 Solving -18x + 15x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -18x + 15x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -18x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-60 + -6x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-60 + -6x + 5x2)' equal to zero and attempt to solve: Simplifying -60 + -6x + 5x2 = 0 Solving -60 + -6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12 + -1.2x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -1.2x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -1.2x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1.2x + x2 = 0 + 12 -1.2x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -1.2x + x2 = 12 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 12 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 12 + 0.36 Combine like terms: 12 + 0.36 = 12.36 0.36 + -1.2x + x2 = 12.36 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 12.36 Calculate the square root of the right side: 3.515679166 Break this problem into two subproblems by setting (x + -0.6) equal to 3.515679166 and -3.515679166.Subproblem 1
x + -0.6 = 3.515679166 Simplifying x + -0.6 = 3.515679166 Reorder the terms: -0.6 + x = 3.515679166 Solving -0.6 + x = 3.515679166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 3.515679166 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 3.515679166 + 0.6 x = 3.515679166 + 0.6 Combine like terms: 3.515679166 + 0.6 = 4.115679166 x = 4.115679166 Simplifying x = 4.115679166Subproblem 2
x + -0.6 = -3.515679166 Simplifying x + -0.6 = -3.515679166 Reorder the terms: -0.6 + x = -3.515679166 Solving -0.6 + x = -3.515679166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -3.515679166 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -3.515679166 + 0.6 x = -3.515679166 + 0.6 Combine like terms: -3.515679166 + 0.6 = -2.915679166 x = -2.915679166 Simplifying x = -2.915679166Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.115679166, -2.915679166}Solution
x = {4.115679166, -2.915679166}
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