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Simplifying 3x(4 + -3x) + 15x = -32 (4 * 3x + -3x * 3x) + 15x = -32 (12x + -9x2) + 15x = -32 Reorder the terms: 12x + 15x + -9x2 = -32 Combine like terms: 12x + 15x = 27x 27x + -9x2 = -32 Solving 27x + -9x2 = -32 Solving for variable 'x'. Reorder the terms: 32 + 27x + -9x2 = -32 + 32 Combine like terms: -32 + 32 = 0 32 + 27x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -3.555555556 + -3x + x2 = 0 Move the constant term to the right: Add '3.555555556' to each side of the equation. -3.555555556 + -3x + 3.555555556 + x2 = 0 + 3.555555556 Reorder the terms: -3.555555556 + 3.555555556 + -3x + x2 = 0 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + -3x + x2 = 0 + 3.555555556 -3x + x2 = 0 + 3.555555556 Combine like terms: 0 + 3.555555556 = 3.555555556 -3x + x2 = 3.555555556 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 = 3.555555556 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 3.555555556 + 2.25 Combine like terms: 3.555555556 + 2.25 = 5.805555556 2.25 + -3x + x2 = 5.805555556 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 5.805555556 Calculate the square root of the right side: 2.409472049 Break this problem into two subproblems by setting (x + -1.5) equal to 2.409472049 and -2.409472049.Subproblem 1
x + -1.5 = 2.409472049 Simplifying x + -1.5 = 2.409472049 Reorder the terms: -1.5 + x = 2.409472049 Solving -1.5 + x = 2.409472049 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 = 2.409472049 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.409472049 + 1.5 x = 2.409472049 + 1.5 Combine like terms: 2.409472049 + 1.5 = 3.909472049 x = 3.909472049 Simplifying x = 3.909472049Subproblem 2
x + -1.5 = -2.409472049 Simplifying x + -1.5 = -2.409472049 Reorder the terms: -1.5 + x = -2.409472049 Solving -1.5 + x = -2.409472049 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 = -2.409472049 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.409472049 + 1.5 x = -2.409472049 + 1.5 Combine like terms: -2.409472049 + 1.5 = -0.909472049 x = -0.909472049 Simplifying x = -0.909472049Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.909472049, -0.909472049}
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