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Simplifying 2x3 + -15x2 + -4x = 0 Reorder the terms: -4x + -15x2 + 2x3 = 0 Solving -4x + -15x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + -15x + 2x2) = 0Subproblem 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 '(-4 + -15x + 2x2)' equal to zero and attempt to solve: Simplifying -4 + -15x + 2x2 = 0 Solving -4 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -7.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -7.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -7.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7.5x + x2 = 0 + 2 -7.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -7.5x + x2 = 2 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 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 2 + 14.0625 Combine like terms: 2 + 14.0625 = 16.0625 14.0625 + -7.5x + x2 = 16.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 16.0625 Calculate the square root of the right side: 4.007804885 Break this problem into two subproblems by setting (x + -3.75) equal to 4.007804885 and -4.007804885.Subproblem 1
x + -3.75 = 4.007804885 Simplifying x + -3.75 = 4.007804885 Reorder the terms: -3.75 + x = 4.007804885 Solving -3.75 + x = 4.007804885 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 = 4.007804885 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 4.007804885 + 3.75 x = 4.007804885 + 3.75 Combine like terms: 4.007804885 + 3.75 = 7.757804885 x = 7.757804885 Simplifying x = 7.757804885Subproblem 2
x + -3.75 = -4.007804885 Simplifying x + -3.75 = -4.007804885 Reorder the terms: -3.75 + x = -4.007804885 Solving -3.75 + x = -4.007804885 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 = -4.007804885 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -4.007804885 + 3.75 x = -4.007804885 + 3.75 Combine like terms: -4.007804885 + 3.75 = -0.257804885 x = -0.257804885 Simplifying x = -0.257804885Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.757804885, -0.257804885}Solution
x = {0, 7.757804885, -0.257804885}
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