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Simplifying -16x2 + 16x + 625 = 0 Reorder the terms: 625 + 16x + -16x2 = 0 Solving 625 + 16x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -39.0625 + -1x + x2 = 0 Move the constant term to the right: Add '39.0625' to each side of the equation. -39.0625 + -1x + 39.0625 + x2 = 0 + 39.0625 Reorder the terms: -39.0625 + 39.0625 + -1x + x2 = 0 + 39.0625 Combine like terms: -39.0625 + 39.0625 = 0.0000 0.0000 + -1x + x2 = 0 + 39.0625 -1x + x2 = 0 + 39.0625 Combine like terms: 0 + 39.0625 = 39.0625 -1x + x2 = 39.0625 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 39.0625 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 39.0625 + 0.25 Combine like terms: 39.0625 + 0.25 = 39.3125 0.25 + -1x + x2 = 39.3125 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 39.3125 Calculate the square root of the right side: 6.269968102 Break this problem into two subproblems by setting (x + -0.5) equal to 6.269968102 and -6.269968102.Subproblem 1
x + -0.5 = 6.269968102 Simplifying x + -0.5 = 6.269968102 Reorder the terms: -0.5 + x = 6.269968102 Solving -0.5 + x = 6.269968102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 6.269968102 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.269968102 + 0.5 x = 6.269968102 + 0.5 Combine like terms: 6.269968102 + 0.5 = 6.769968102 x = 6.769968102 Simplifying x = 6.769968102Subproblem 2
x + -0.5 = -6.269968102 Simplifying x + -0.5 = -6.269968102 Reorder the terms: -0.5 + x = -6.269968102 Solving -0.5 + x = -6.269968102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -6.269968102 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.269968102 + 0.5 x = -6.269968102 + 0.5 Combine like terms: -6.269968102 + 0.5 = -5.769968102 x = -5.769968102 Simplifying x = -5.769968102Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.769968102, -5.769968102}
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