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Simplifying 8x2 + 1x + -64 = 0 Reorder the terms: -64 + 1x + 8x2 = 0 Solving -64 + 1x + 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 + 0.125x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 0.125x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 0.125x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 0.125x + x2 = 0 + 8 0.125x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 0.125x + x2 = 8 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 = 8 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 8 + 0.00390625 Combine like terms: 8 + 0.00390625 = 8.00390625 0.00390625 + 0.125x + x2 = 8.00390625 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 8.00390625 Calculate the square root of the right side: 2.829117574 Break this problem into two subproblems by setting (x + 0.0625) equal to 2.829117574 and -2.829117574.Subproblem 1
x + 0.0625 = 2.829117574 Simplifying x + 0.0625 = 2.829117574 Reorder the terms: 0.0625 + x = 2.829117574 Solving 0.0625 + x = 2.829117574 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 = 2.829117574 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 2.829117574 + -0.0625 x = 2.829117574 + -0.0625 Combine like terms: 2.829117574 + -0.0625 = 2.766617574 x = 2.766617574 Simplifying x = 2.766617574Subproblem 2
x + 0.0625 = -2.829117574 Simplifying x + 0.0625 = -2.829117574 Reorder the terms: 0.0625 + x = -2.829117574 Solving 0.0625 + x = -2.829117574 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 = -2.829117574 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -2.829117574 + -0.0625 x = -2.829117574 + -0.0625 Combine like terms: -2.829117574 + -0.0625 = -2.891617574 x = -2.891617574 Simplifying x = -2.891617574Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.766617574, -2.891617574}
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