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Simplifying -16x2 + 10x + 625 = 0 Reorder the terms: 625 + 10x + -16x2 = 0 Solving 625 + 10x + -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 + -0.625x + x2 = 0 Move the constant term to the right: Add '39.0625' to each side of the equation. -39.0625 + -0.625x + 39.0625 + x2 = 0 + 39.0625 Reorder the terms: -39.0625 + 39.0625 + -0.625x + x2 = 0 + 39.0625 Combine like terms: -39.0625 + 39.0625 = 0.0000 0.0000 + -0.625x + x2 = 0 + 39.0625 -0.625x + x2 = 0 + 39.0625 Combine like terms: 0 + 39.0625 = 39.0625 -0.625x + x2 = 39.0625 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 39.0625 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 39.0625 + 0.09765625 Combine like terms: 39.0625 + 0.09765625 = 39.16015625 0.09765625 + -0.625x + x2 = 39.16015625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 39.16015625 Calculate the square root of the right side: 6.257807623 Break this problem into two subproblems by setting (x + -0.3125) equal to 6.257807623 and -6.257807623.Subproblem 1
x + -0.3125 = 6.257807623 Simplifying x + -0.3125 = 6.257807623 Reorder the terms: -0.3125 + x = 6.257807623 Solving -0.3125 + x = 6.257807623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 6.257807623 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 6.257807623 + 0.3125 x = 6.257807623 + 0.3125 Combine like terms: 6.257807623 + 0.3125 = 6.570307623 x = 6.570307623 Simplifying x = 6.570307623Subproblem 2
x + -0.3125 = -6.257807623 Simplifying x + -0.3125 = -6.257807623 Reorder the terms: -0.3125 + x = -6.257807623 Solving -0.3125 + x = -6.257807623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -6.257807623 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -6.257807623 + 0.3125 x = -6.257807623 + 0.3125 Combine like terms: -6.257807623 + 0.3125 = -5.945307623 x = -5.945307623 Simplifying x = -5.945307623Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.570307623, -5.945307623}
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