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Simplifying 2x4 + -1x3 + -5x2 = 0 Reorder the terms: -5x2 + -1x3 + 2x4 = 0 Solving -5x2 + -1x3 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-5 + -1x + 2x2) = 0Subproblem 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 '(-5 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -5 + -1x + 2x2 = 0 Solving -5 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.5x + x2 = 0 + 2.5 -0.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.5x + x2 = 2.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 2.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 2.5 + 0.0625 Combine like terms: 2.5 + 0.0625 = 2.5625 0.0625 + -0.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -0.25) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -0.25 = 1.600781059 Simplifying x + -0.25 = 1.600781059 Reorder the terms: -0.25 + x = 1.600781059 Solving -0.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.600781059 + 0.25 x = 1.600781059 + 0.25 Combine like terms: 1.600781059 + 0.25 = 1.850781059 x = 1.850781059 Simplifying x = 1.850781059Subproblem 2
x + -0.25 = -1.600781059 Simplifying x + -0.25 = -1.600781059 Reorder the terms: -0.25 + x = -1.600781059 Solving -0.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.600781059 + 0.25 x = -1.600781059 + 0.25 Combine like terms: -1.600781059 + 0.25 = -1.350781059 x = -1.350781059 Simplifying x = -1.350781059Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.850781059, -1.350781059}Solution
x = {0, 1.850781059, -1.350781059}
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