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Simplifying 0 = -16x2 + 4013x + 3250 Reorder the terms: 0 = 3250 + 4013x + -16x2 Solving 0 = 3250 + 4013x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -3250 = -3250 -3250 + -4013x + 16x2 = 3250 + 4013x + -16x2 + -3250 + -4013x + 16x2 Reorder the terms: -3250 + -4013x + 16x2 = 3250 + -3250 + 4013x + -4013x + -16x2 + 16x2 Combine like terms: 3250 + -3250 = 0 -3250 + -4013x + 16x2 = 0 + 4013x + -4013x + -16x2 + 16x2 -3250 + -4013x + 16x2 = 4013x + -4013x + -16x2 + 16x2 Combine like terms: 4013x + -4013x = 0 -3250 + -4013x + 16x2 = 0 + -16x2 + 16x2 -3250 + -4013x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -3250 + -4013x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -203.125 + -250.8125x + x2 = 0 Move the constant term to the right: Add '203.125' to each side of the equation. -203.125 + -250.8125x + 203.125 + x2 = 0 + 203.125 Reorder the terms: -203.125 + 203.125 + -250.8125x + x2 = 0 + 203.125 Combine like terms: -203.125 + 203.125 = 0.000 0.000 + -250.8125x + x2 = 0 + 203.125 -250.8125x + x2 = 0 + 203.125 Combine like terms: 0 + 203.125 = 203.125 -250.8125x + x2 = 203.125 The x term is -250.8125x. Take half its coefficient (-125.40625). Square it (15726.72754) and add it to both sides. Add '15726.72754' to each side of the equation. -250.8125x + 15726.72754 + x2 = 203.125 + 15726.72754 Reorder the terms: 15726.72754 + -250.8125x + x2 = 203.125 + 15726.72754 Combine like terms: 203.125 + 15726.72754 = 15929.85254 15726.72754 + -250.8125x + x2 = 15929.85254 Factor a perfect square on the left side: (x + -125.40625)(x + -125.40625) = 15929.85254 Calculate the square root of the right side: 126.21351964 Break this problem into two subproblems by setting (x + -125.40625) equal to 126.21351964 and -126.21351964.Subproblem 1
x + -125.40625 = 126.21351964 Simplifying x + -125.40625 = 126.21351964 Reorder the terms: -125.40625 + x = 126.21351964 Solving -125.40625 + x = 126.21351964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125.40625' to each side of the equation. -125.40625 + 125.40625 + x = 126.21351964 + 125.40625 Combine like terms: -125.40625 + 125.40625 = 0.00000 0.00000 + x = 126.21351964 + 125.40625 x = 126.21351964 + 125.40625 Combine like terms: 126.21351964 + 125.40625 = 251.61976964 x = 251.61976964 Simplifying x = 251.61976964Subproblem 2
x + -125.40625 = -126.21351964 Simplifying x + -125.40625 = -126.21351964 Reorder the terms: -125.40625 + x = -126.21351964 Solving -125.40625 + x = -126.21351964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125.40625' to each side of the equation. -125.40625 + 125.40625 + x = -126.21351964 + 125.40625 Combine like terms: -125.40625 + 125.40625 = 0.00000 0.00000 + x = -126.21351964 + 125.40625 x = -126.21351964 + 125.40625 Combine like terms: -126.21351964 + 125.40625 = -0.80726964 x = -0.80726964 Simplifying x = -0.80726964Solution
The solution to the problem is based on the solutions from the subproblems. x = {251.61976964, -0.80726964}
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