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Simplifying 4x2 + -2x = 80 Reorder the terms: -2x + 4x2 = 80 Solving -2x + 4x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + -2x + 4x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-40 + -1x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -40 + -1x + 2x2 = 0 Solving -40 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -20 + -0.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -0.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -0.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -0.5x + x2 = 0 + 20 -0.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -0.5x + x2 = 20 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 = 20 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 20 + 0.0625 Combine like terms: 20 + 0.0625 = 20.0625 0.0625 + -0.5x + x2 = 20.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (x + -0.25) equal to 4.479118217 and -4.479118217.Subproblem 1
x + -0.25 = 4.479118217 Simplifying x + -0.25 = 4.479118217 Reorder the terms: -0.25 + x = 4.479118217 Solving -0.25 + x = 4.479118217 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 = 4.479118217 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 4.479118217 + 0.25 x = 4.479118217 + 0.25 Combine like terms: 4.479118217 + 0.25 = 4.729118217 x = 4.729118217 Simplifying x = 4.729118217Subproblem 2
x + -0.25 = -4.479118217 Simplifying x + -0.25 = -4.479118217 Reorder the terms: -0.25 + x = -4.479118217 Solving -0.25 + x = -4.479118217 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 = -4.479118217 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -4.479118217 + 0.25 x = -4.479118217 + 0.25 Combine like terms: -4.479118217 + 0.25 = -4.229118217 x = -4.229118217 Simplifying x = -4.229118217Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.729118217, -4.229118217}Solution
x = {4.729118217, -4.229118217}
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