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Simplifying 25x2 + 2x3 + -4x = 0 Reorder the terms: -4x + 25x2 + 2x3 = 0 Solving -4x + 25x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 25x + 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 + 25x + 2x2)' equal to zero and attempt to solve: Simplifying -4 + 25x + 2x2 = 0 Solving -4 + 25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 12.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 12.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 12.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 12.5x + x2 = 0 + 2 12.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 12.5x + x2 = 2 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = 2 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 2 + 39.0625 Combine like terms: 2 + 39.0625 = 41.0625 39.0625 + 12.5x + x2 = 41.0625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 41.0625 Calculate the square root of the right side: 6.408002809 Break this problem into two subproblems by setting (x + 6.25) equal to 6.408002809 and -6.408002809.Subproblem 1
x + 6.25 = 6.408002809 Simplifying x + 6.25 = 6.408002809 Reorder the terms: 6.25 + x = 6.408002809 Solving 6.25 + x = 6.408002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 6.408002809 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 6.408002809 + -6.25 x = 6.408002809 + -6.25 Combine like terms: 6.408002809 + -6.25 = 0.158002809 x = 0.158002809 Simplifying x = 0.158002809Subproblem 2
x + 6.25 = -6.408002809 Simplifying x + 6.25 = -6.408002809 Reorder the terms: 6.25 + x = -6.408002809 Solving 6.25 + x = -6.408002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -6.408002809 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -6.408002809 + -6.25 x = -6.408002809 + -6.25 Combine like terms: -6.408002809 + -6.25 = -12.658002809 x = -12.658002809 Simplifying x = -12.658002809Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.158002809, -12.658002809}Solution
x = {0, 0.158002809, -12.658002809}
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