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Simplifying 50 = -16x2 + 63x Reorder the terms: 50 = 63x + -16x2 Solving 50 = 63x + -16x2 Solving for variable 'x'. Reorder the terms: 50 + -63x + 16x2 = 63x + -63x + -16x2 + 16x2 Combine like terms: 63x + -63x = 0 50 + -63x + 16x2 = 0 + -16x2 + 16x2 50 + -63x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 50 + -63x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.125 + -3.9375x + x2 = 0 Move the constant term to the right: Add '-3.125' to each side of the equation. 3.125 + -3.9375x + -3.125 + x2 = 0 + -3.125 Reorder the terms: 3.125 + -3.125 + -3.9375x + x2 = 0 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + -3.9375x + x2 = 0 + -3.125 -3.9375x + x2 = 0 + -3.125 Combine like terms: 0 + -3.125 = -3.125 -3.9375x + x2 = -3.125 The x term is -3.9375x. Take half its coefficient (-1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. -3.9375x + 3.875976563 + x2 = -3.125 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375x + x2 = -3.125 + 3.875976563 Combine like terms: -3.125 + 3.875976563 = 0.750976563 3.875976563 + -3.9375x + x2 = 0.750976563 Factor a perfect square on the left side: (x + -1.96875)(x + -1.96875) = 0.750976563 Calculate the square root of the right side: 0.866589039 Break this problem into two subproblems by setting (x + -1.96875) equal to 0.866589039 and -0.866589039.Subproblem 1
x + -1.96875 = 0.866589039 Simplifying x + -1.96875 = 0.866589039 Reorder the terms: -1.96875 + x = 0.866589039 Solving -1.96875 + x = 0.866589039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = 0.866589039 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = 0.866589039 + 1.96875 x = 0.866589039 + 1.96875 Combine like terms: 0.866589039 + 1.96875 = 2.835339039 x = 2.835339039 Simplifying x = 2.835339039Subproblem 2
x + -1.96875 = -0.866589039 Simplifying x + -1.96875 = -0.866589039 Reorder the terms: -1.96875 + x = -0.866589039 Solving -1.96875 + x = -0.866589039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + x = -0.866589039 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = -0.866589039 + 1.96875 x = -0.866589039 + 1.96875 Combine like terms: -0.866589039 + 1.96875 = 1.102160961 x = 1.102160961 Simplifying x = 1.102160961Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.835339039, 1.102160961}
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