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Simplifying -16x2 + -2x + 765 = 0 Reorder the terms: 765 + -2x + -16x2 = 0 Solving 765 + -2x + -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'. -47.8125 + 0.125x + x2 = 0 Move the constant term to the right: Add '47.8125' to each side of the equation. -47.8125 + 0.125x + 47.8125 + x2 = 0 + 47.8125 Reorder the terms: -47.8125 + 47.8125 + 0.125x + x2 = 0 + 47.8125 Combine like terms: -47.8125 + 47.8125 = 0.0000 0.0000 + 0.125x + x2 = 0 + 47.8125 0.125x + x2 = 0 + 47.8125 Combine like terms: 0 + 47.8125 = 47.8125 0.125x + x2 = 47.8125 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = 47.8125 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 47.8125 + 0.00390625 Combine like terms: 47.8125 + 0.00390625 = 47.81640625 0.00390625 + 0.125x + x2 = 47.81640625 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 47.81640625 Calculate the square root of the right side: 6.914940799 Break this problem into two subproblems by setting (x + 0.0625) equal to 6.914940799 and -6.914940799.Subproblem 1
x + 0.0625 = 6.914940799 Simplifying x + 0.0625 = 6.914940799 Reorder the terms: 0.0625 + x = 6.914940799 Solving 0.0625 + x = 6.914940799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 6.914940799 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 6.914940799 + -0.0625 x = 6.914940799 + -0.0625 Combine like terms: 6.914940799 + -0.0625 = 6.852440799 x = 6.852440799 Simplifying x = 6.852440799Subproblem 2
x + 0.0625 = -6.914940799 Simplifying x + 0.0625 = -6.914940799 Reorder the terms: 0.0625 + x = -6.914940799 Solving 0.0625 + x = -6.914940799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -6.914940799 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -6.914940799 + -0.0625 x = -6.914940799 + -0.0625 Combine like terms: -6.914940799 + -0.0625 = -6.977440799 x = -6.977440799 Simplifying x = -6.977440799Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.852440799, -6.977440799}
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