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Simplifying -16x2 + 64x + 40 = x Reorder the terms: 40 + 64x + -16x2 = x Solving 40 + 64x + -16x2 = x Solving for variable 'x'. Reorder the terms: 40 + 64x + -1x + -16x2 = x + -1x Combine like terms: 64x + -1x = 63x 40 + 63x + -16x2 = x + -1x Combine like terms: x + -1x = 0 40 + 63x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.5 + -3.9375x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3.9375x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3.9375x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3.9375x + x2 = 0 + 2.5 -3.9375x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3.9375x + x2 = 2.5 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 = 2.5 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375x + x2 = 2.5 + 3.875976563 Combine like terms: 2.5 + 3.875976563 = 6.375976563 3.875976563 + -3.9375x + x2 = 6.375976563 Factor a perfect square on the left side: (x + -1.96875)(x + -1.96875) = 6.375976563 Calculate the square root of the right side: 2.525069615 Break this problem into two subproblems by setting (x + -1.96875) equal to 2.525069615 and -2.525069615.Subproblem 1
x + -1.96875 = 2.525069615 Simplifying x + -1.96875 = 2.525069615 Reorder the terms: -1.96875 + x = 2.525069615 Solving -1.96875 + x = 2.525069615 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 = 2.525069615 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = 2.525069615 + 1.96875 x = 2.525069615 + 1.96875 Combine like terms: 2.525069615 + 1.96875 = 4.493819615 x = 4.493819615 Simplifying x = 4.493819615Subproblem 2
x + -1.96875 = -2.525069615 Simplifying x + -1.96875 = -2.525069615 Reorder the terms: -1.96875 + x = -2.525069615 Solving -1.96875 + x = -2.525069615 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 = -2.525069615 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + x = -2.525069615 + 1.96875 x = -2.525069615 + 1.96875 Combine like terms: -2.525069615 + 1.96875 = -0.556319615 x = -0.556319615 Simplifying x = -0.556319615Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.493819615, -0.556319615}
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