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Simplifying 16x2 + -20x = 148 Reorder the terms: -20x + 16x2 = 148 Solving -20x + 16x2 = 148 Solving for variable 'x'. Reorder the terms: -148 + -20x + 16x2 = 148 + -148 Combine like terms: 148 + -148 = 0 -148 + -20x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-37 + -5x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-37 + -5x + 4x2)' equal to zero and attempt to solve: Simplifying -37 + -5x + 4x2 = 0 Solving -37 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.25 + -1.25x + x2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + -1.25x + 9.25 + x2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + -1.25x + x2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + -1.25x + x2 = 0 + 9.25 -1.25x + x2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 -1.25x + x2 = 9.25 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 9.25 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 9.25 + 0.390625 Combine like terms: 9.25 + 0.390625 = 9.640625 0.390625 + -1.25x + x2 = 9.640625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 9.640625 Calculate the square root of the right side: 3.104935587 Break this problem into two subproblems by setting (x + -0.625) equal to 3.104935587 and -3.104935587.Subproblem 1
x + -0.625 = 3.104935587 Simplifying x + -0.625 = 3.104935587 Reorder the terms: -0.625 + x = 3.104935587 Solving -0.625 + x = 3.104935587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 3.104935587 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 3.104935587 + 0.625 x = 3.104935587 + 0.625 Combine like terms: 3.104935587 + 0.625 = 3.729935587 x = 3.729935587 Simplifying x = 3.729935587Subproblem 2
x + -0.625 = -3.104935587 Simplifying x + -0.625 = -3.104935587 Reorder the terms: -0.625 + x = -3.104935587 Solving -0.625 + x = -3.104935587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -3.104935587 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -3.104935587 + 0.625 x = -3.104935587 + 0.625 Combine like terms: -3.104935587 + 0.625 = -2.479935587 x = -2.479935587 Simplifying x = -2.479935587Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.729935587, -2.479935587}Solution
x = {3.729935587, -2.479935587}
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