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Simplifying 64x2 + 36x + -25 = 0 Reorder the terms: -25 + 36x + 64x2 = 0 Solving -25 + 36x + 64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.390625 + 0.5625x + x2 = 0 Move the constant term to the right: Add '0.390625' to each side of the equation. -0.390625 + 0.5625x + 0.390625 + x2 = 0 + 0.390625 Reorder the terms: -0.390625 + 0.390625 + 0.5625x + x2 = 0 + 0.390625 Combine like terms: -0.390625 + 0.390625 = 0.000000 0.000000 + 0.5625x + x2 = 0 + 0.390625 0.5625x + x2 = 0 + 0.390625 Combine like terms: 0 + 0.390625 = 0.390625 0.5625x + x2 = 0.390625 The x term is 0.5625x. Take half its coefficient (0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. 0.5625x + 0.0791015625 + x2 = 0.390625 + 0.0791015625 Reorder the terms: 0.0791015625 + 0.5625x + x2 = 0.390625 + 0.0791015625 Combine like terms: 0.390625 + 0.0791015625 = 0.4697265625 0.0791015625 + 0.5625x + x2 = 0.4697265625 Factor a perfect square on the left side: (x + 0.28125)(x + 0.28125) = 0.4697265625 Calculate the square root of the right side: 0.685366006 Break this problem into two subproblems by setting (x + 0.28125) equal to 0.685366006 and -0.685366006.Subproblem 1
x + 0.28125 = 0.685366006 Simplifying x + 0.28125 = 0.685366006 Reorder the terms: 0.28125 + x = 0.685366006 Solving 0.28125 + x = 0.685366006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = 0.685366006 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = 0.685366006 + -0.28125 x = 0.685366006 + -0.28125 Combine like terms: 0.685366006 + -0.28125 = 0.404116006 x = 0.404116006 Simplifying x = 0.404116006Subproblem 2
x + 0.28125 = -0.685366006 Simplifying x + 0.28125 = -0.685366006 Reorder the terms: 0.28125 + x = -0.685366006 Solving 0.28125 + x = -0.685366006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = -0.685366006 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = -0.685366006 + -0.28125 x = -0.685366006 + -0.28125 Combine like terms: -0.685366006 + -0.28125 = -0.966616006 x = -0.966616006 Simplifying x = -0.966616006Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.404116006, -0.966616006}
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