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Simplifying 64x2 + 80x + 15 = 0 Reorder the terms: 15 + 80x + 64x2 = 0 Solving 15 + 80x + 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'. 0.234375 + 1.25x + x2 = 0 Move the constant term to the right: Add '-0.234375' to each side of the equation. 0.234375 + 1.25x + -0.234375 + x2 = 0 + -0.234375 Reorder the terms: 0.234375 + -0.234375 + 1.25x + x2 = 0 + -0.234375 Combine like terms: 0.234375 + -0.234375 = 0.000000 0.000000 + 1.25x + x2 = 0 + -0.234375 1.25x + x2 = 0 + -0.234375 Combine like terms: 0 + -0.234375 = -0.234375 1.25x + x2 = -0.234375 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -0.234375 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -0.234375 + 0.390625 Combine like terms: -0.234375 + 0.390625 = 0.15625 0.390625 + 1.25x + x2 = 0.15625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 0.15625 Calculate the square root of the right side: 0.395284708 Break this problem into two subproblems by setting (x + 0.625) equal to 0.395284708 and -0.395284708.Subproblem 1
x + 0.625 = 0.395284708 Simplifying x + 0.625 = 0.395284708 Reorder the terms: 0.625 + x = 0.395284708 Solving 0.625 + x = 0.395284708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 0.395284708 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 0.395284708 + -0.625 x = 0.395284708 + -0.625 Combine like terms: 0.395284708 + -0.625 = -0.229715292 x = -0.229715292 Simplifying x = -0.229715292Subproblem 2
x + 0.625 = -0.395284708 Simplifying x + 0.625 = -0.395284708 Reorder the terms: 0.625 + x = -0.395284708 Solving 0.625 + x = -0.395284708 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -0.395284708 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -0.395284708 + -0.625 x = -0.395284708 + -0.625 Combine like terms: -0.395284708 + -0.625 = -1.020284708 x = -1.020284708 Simplifying x = -1.020284708Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.229715292, -1.020284708}
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