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Simplifying -3(3x + 15)(10 + x) = 35 Reorder the terms: -3(15 + 3x)(10 + x) = 35 Multiply (15 + 3x) * (10 + x) -3(15(10 + x) + 3x * (10 + x)) = 35 -3((10 * 15 + x * 15) + 3x * (10 + x)) = 35 -3((150 + 15x) + 3x * (10 + x)) = 35 -3(150 + 15x + (10 * 3x + x * 3x)) = 35 -3(150 + 15x + (30x + 3x2)) = 35 Combine like terms: 15x + 30x = 45x -3(150 + 45x + 3x2) = 35 (150 * -3 + 45x * -3 + 3x2 * -3) = 35 (-450 + -135x + -9x2) = 35 Solving -450 + -135x + -9x2 = 35 Solving for variable 'x'. Reorder the terms: -450 + -35 + -135x + -9x2 = 35 + -35 Combine like terms: -450 + -35 = -485 -485 + -135x + -9x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -485 + -135x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(485 + 135x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(485 + 135x + 9x2)' equal to zero and attempt to solve: Simplifying 485 + 135x + 9x2 = 0 Solving 485 + 135x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 53.88888889 + 15x + x2 = 0 Move the constant term to the right: Add '-53.88888889' to each side of the equation. 53.88888889 + 15x + -53.88888889 + x2 = 0 + -53.88888889 Reorder the terms: 53.88888889 + -53.88888889 + 15x + x2 = 0 + -53.88888889 Combine like terms: 53.88888889 + -53.88888889 = 0.00000000 0.00000000 + 15x + x2 = 0 + -53.88888889 15x + x2 = 0 + -53.88888889 Combine like terms: 0 + -53.88888889 = -53.88888889 15x + x2 = -53.88888889 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -53.88888889 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -53.88888889 + 56.25 Combine like terms: -53.88888889 + 56.25 = 2.36111111 56.25 + 15x + x2 = 2.36111111 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 2.36111111 Calculate the square root of the right side: 1.536590743 Break this problem into two subproblems by setting (x + 7.5) equal to 1.536590743 and -1.536590743.Subproblem 1
x + 7.5 = 1.536590743 Simplifying x + 7.5 = 1.536590743 Reorder the terms: 7.5 + x = 1.536590743 Solving 7.5 + x = 1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 1.536590743 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 1.536590743 + -7.5 x = 1.536590743 + -7.5 Combine like terms: 1.536590743 + -7.5 = -5.963409257 x = -5.963409257 Simplifying x = -5.963409257Subproblem 2
x + 7.5 = -1.536590743 Simplifying x + 7.5 = -1.536590743 Reorder the terms: 7.5 + x = -1.536590743 Solving 7.5 + x = -1.536590743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -1.536590743 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -1.536590743 + -7.5 x = -1.536590743 + -7.5 Combine like terms: -1.536590743 + -7.5 = -9.036590743 x = -9.036590743 Simplifying x = -9.036590743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.963409257, -9.036590743}Solution
x = {-5.963409257, -9.036590743}
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