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Simplifying 6x3 + 45x2 + 15x = 0 Reorder the terms: 15x + 45x2 + 6x3 = 0 Solving 15x + 45x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(5 + 15x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5 + 15x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 15x + 2x2 = 0 Solving 5 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 7.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 7.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 7.5x + x2 = 0 + -2.5 7.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 7.5x + x2 = -2.5 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = -2.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -2.5 + 14.0625 Combine like terms: -2.5 + 14.0625 = 11.5625 14.0625 + 7.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + 3.75) equal to 3.400367627 and -3.400367627.Subproblem 1
x + 3.75 = 3.400367627 Simplifying x + 3.75 = 3.400367627 Reorder the terms: 3.75 + x = 3.400367627 Solving 3.75 + x = 3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 3.400367627 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 3.400367627 + -3.75 x = 3.400367627 + -3.75 Combine like terms: 3.400367627 + -3.75 = -0.349632373 x = -0.349632373 Simplifying x = -0.349632373Subproblem 2
x + 3.75 = -3.400367627 Simplifying x + 3.75 = -3.400367627 Reorder the terms: 3.75 + x = -3.400367627 Solving 3.75 + x = -3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -3.400367627 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -3.400367627 + -3.75 x = -3.400367627 + -3.75 Combine like terms: -3.400367627 + -3.75 = -7.150367627 x = -7.150367627 Simplifying x = -7.150367627Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.349632373, -7.150367627}Solution
x = {0, -0.349632373, -7.150367627}
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