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Simplifying 8x2 + 65x + 64 = 0 Reorder the terms: 64 + 65x + 8x2 = 0 Solving 64 + 65x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 8 + 8.125x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 8.125x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 8.125x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 8.125x + x2 = 0 + -8 8.125x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 8.125x + x2 = -8 The x term is 8.125x. Take half its coefficient (4.0625). Square it (16.50390625) and add it to both sides. Add '16.50390625' to each side of the equation. 8.125x + 16.50390625 + x2 = -8 + 16.50390625 Reorder the terms: 16.50390625 + 8.125x + x2 = -8 + 16.50390625 Combine like terms: -8 + 16.50390625 = 8.50390625 16.50390625 + 8.125x + x2 = 8.50390625 Factor a perfect square on the left side: (x + 4.0625)(x + 4.0625) = 8.50390625 Calculate the square root of the right side: 2.916145787 Break this problem into two subproblems by setting (x + 4.0625) equal to 2.916145787 and -2.916145787.Subproblem 1
x + 4.0625 = 2.916145787 Simplifying x + 4.0625 = 2.916145787 Reorder the terms: 4.0625 + x = 2.916145787 Solving 4.0625 + x = 2.916145787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.0625' to each side of the equation. 4.0625 + -4.0625 + x = 2.916145787 + -4.0625 Combine like terms: 4.0625 + -4.0625 = 0.0000 0.0000 + x = 2.916145787 + -4.0625 x = 2.916145787 + -4.0625 Combine like terms: 2.916145787 + -4.0625 = -1.146354213 x = -1.146354213 Simplifying x = -1.146354213Subproblem 2
x + 4.0625 = -2.916145787 Simplifying x + 4.0625 = -2.916145787 Reorder the terms: 4.0625 + x = -2.916145787 Solving 4.0625 + x = -2.916145787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.0625' to each side of the equation. 4.0625 + -4.0625 + x = -2.916145787 + -4.0625 Combine like terms: 4.0625 + -4.0625 = 0.0000 0.0000 + x = -2.916145787 + -4.0625 x = -2.916145787 + -4.0625 Combine like terms: -2.916145787 + -4.0625 = -6.978645787 x = -6.978645787 Simplifying x = -6.978645787Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.146354213, -6.978645787}
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