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Simplifying 156.25 = -16x2 + 100x Reorder the terms: 156.25 = 100x + -16x2 Solving 156.25 = 100x + -16x2 Solving for variable 'x'. Reorder the terms: 156.25 + -100x + 16x2 = 100x + -100x + -16x2 + 16x2 Combine like terms: 100x + -100x = 0 156.25 + -100x + 16x2 = 0 + -16x2 + 16x2 156.25 + -100x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 156.25 + -100x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 9.765625 + -6.25x + x2 = 0 Move the constant term to the right: Add '-9.765625' to each side of the equation. 9.765625 + -6.25x + -9.765625 + x2 = 0 + -9.765625 Reorder the terms: 9.765625 + -9.765625 + -6.25x + x2 = 0 + -9.765625 Combine like terms: 9.765625 + -9.765625 = 0.000000 0.000000 + -6.25x + x2 = 0 + -9.765625 -6.25x + x2 = 0 + -9.765625 Combine like terms: 0 + -9.765625 = -9.765625 -6.25x + x2 = -9.765625 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -9.765625 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -9.765625 + 9.765625 Combine like terms: -9.765625 + 9.765625 = 0.000000 9.765625 + -6.25x + x2 = 0.000000 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 0.000000 Calculate the square root of the right side: 0.000000 Break this problem into two subproblems by setting (x + -3.125) equal to 0.000000 and 0.000000.Subproblem 1
x + -3.125 = 0.000000 Simplifying x + -3.125 = 0.000000 Reorder the terms: -3.125 + x = 0.000000 Solving -3.125 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 0.000000 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 0.000000 + 3.125 x = 0.000000 + 3.125 Combine like terms: 0.000000 + 3.125 = 3.125 x = 3.125 Simplifying x = 3.125Subproblem 2
x + -3.125 = 0.000000 Simplifying x + -3.125 = 0.000000 Reorder the terms: -3.125 + x = 0.000000 Solving -3.125 + x = 0.000000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 0.000000 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 0.000000 + 3.125 x = 0.000000 + 3.125 Combine like terms: 0.000000 + 3.125 = 3.125 x = 3.125 Simplifying x = 3.125Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.125, 3.125}
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