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Simplifying -5000x4 + 6500x2 + 3000 = 0 Reorder the terms: 3000 + 6500x2 + -5000x4 = 0 Solving 3000 + 6500x2 + -5000x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '500'. 500(6 + 13x2 + -10x4) = 0 Ignore the factor 500.Subproblem 1
Set the factor '(6 + 13x2 + -10x4)' equal to zero and attempt to solve: Simplifying 6 + 13x2 + -10x4 = 0 Solving 6 + 13x2 + -10x4 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.6 + -1.3x2 + x4 = 0.0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.3x2 + 0.6 + x4 = 0.0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.3x2 + x4 = 0.0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.3x2 + x4 = 0.0 + 0.6 -1.3x2 + x4 = 0.0 + 0.6 Combine like terms: 0.0 + 0.6 = 0.6 -1.3x2 + x4 = 0.6 The x term is -1.3x2. Take half its coefficient (-0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. -1.3x2 + 0.4225 + x4 = 0.6 + 0.4225 Reorder the terms: 0.4225 + -1.3x2 + x4 = 0.6 + 0.4225 Combine like terms: 0.6 + 0.4225 = 1.0225 0.4225 + -1.3x2 + x4 = 1.0225 Factor a perfect square on the left side: (x2 + -0.65)(x2 + -0.65) = 1.0225 Calculate the square root of the right side: 1.011187421 Break this problem into two subproblems by setting (x2 + -0.65) equal to 1.011187421 and -1.011187421.Subproblem 1
x2 + -0.65 = 1.011187421 Simplifying x2 + -0.65 = 1.011187421 Reorder the terms: -0.65 + x2 = 1.011187421 Solving -0.65 + x2 = 1.011187421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x2 = 1.011187421 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x2 = 1.011187421 + 0.65 x2 = 1.011187421 + 0.65 Combine like terms: 1.011187421 + 0.65 = 1.661187421 x2 = 1.661187421 Simplifying x2 = 1.661187421 Take the square root of each side: x = {-1.288870599, 1.288870599}Subproblem 2
x2 + -0.65 = -1.011187421 Simplifying x2 + -0.65 = -1.011187421 Reorder the terms: -0.65 + x2 = -1.011187421 Solving -0.65 + x2 = -1.011187421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65' to each side of the equation. -0.65 + 0.65 + x2 = -1.011187421 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + x2 = -1.011187421 + 0.65 x2 = -1.011187421 + 0.65 Combine like terms: -1.011187421 + 0.65 = -0.361187421 x2 = -0.361187421 Simplifying x2 = -0.361187421 Reorder the terms: 0.361187421 + x2 = -0.361187421 + 0.361187421 Combine like terms: -0.361187421 + 0.361187421 = 0.000000000 0.361187421 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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