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Simplifying -5x4 + 25x3 + 10x2 = 0 Reorder the terms: 10x2 + 25x3 + -5x4 = 0 Solving 10x2 + 25x3 + -5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(2 + 5x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(2 + 5x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + 5x + -1x2 = 0 Solving 2 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5x + x2 = 0 + 2 -5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -5x + x2 = 2 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 2 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + -5x + x2 = 8.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + -2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + -2.5 = 2.872281323 Simplifying x + -2.5 = 2.872281323 Reorder the terms: -2.5 + x = 2.872281323 Solving -2.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.872281323 + 2.5 x = 2.872281323 + 2.5 Combine like terms: 2.872281323 + 2.5 = 5.372281323 x = 5.372281323 Simplifying x = 5.372281323Subproblem 2
x + -2.5 = -2.872281323 Simplifying x + -2.5 = -2.872281323 Reorder the terms: -2.5 + x = -2.872281323 Solving -2.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.872281323 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.872281323 + 2.5 x = -2.872281323 + 2.5 Combine like terms: -2.872281323 + 2.5 = -0.372281323 x = -0.372281323 Simplifying x = -0.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.372281323, -0.372281323}Solution
x = {0, 5.372281323, -0.372281323}
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