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Simplifying x3 + 15x2 + -53x = 0 Reorder the terms: -53x + 15x2 + x3 = 0 Solving -53x + 15x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-53 + 15x + x2) = 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 '(-53 + 15x + x2)' equal to zero and attempt to solve: Simplifying -53 + 15x + x2 = 0 Solving -53 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + 15x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + 15x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 15x + x2 = 0 + 53 15x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 15x + x2 = 53 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 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 53 + 56.25 Combine like terms: 53 + 56.25 = 109.25 56.25 + 15x + x2 = 109.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 109.25 Calculate the square root of the right side: 10.45227248 Break this problem into two subproblems by setting (x + 7.5) equal to 10.45227248 and -10.45227248.Subproblem 1
x + 7.5 = 10.45227248 Simplifying x + 7.5 = 10.45227248 Reorder the terms: 7.5 + x = 10.45227248 Solving 7.5 + x = 10.45227248 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 = 10.45227248 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 10.45227248 + -7.5 x = 10.45227248 + -7.5 Combine like terms: 10.45227248 + -7.5 = 2.95227248 x = 2.95227248 Simplifying x = 2.95227248Subproblem 2
x + 7.5 = -10.45227248 Simplifying x + 7.5 = -10.45227248 Reorder the terms: 7.5 + x = -10.45227248 Solving 7.5 + x = -10.45227248 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 = -10.45227248 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -10.45227248 + -7.5 x = -10.45227248 + -7.5 Combine like terms: -10.45227248 + -7.5 = -17.95227248 x = -17.95227248 Simplifying x = -17.95227248Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.95227248, -17.95227248}Solution
x = {0, 2.95227248, -17.95227248}
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