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Simplifying 0.6(x + 8)(x + 8) + -66 = 0 Reorder the terms: 0.6(8 + x)(x + 8) + -66 = 0 Reorder the terms: 0.6(8 + x)(8 + x) + -66 = 0 Multiply (8 + x) * (8 + x) 0.6(8(8 + x) + x(8 + x)) + -66 = 0 0.6((8 * 8 + x * 8) + x(8 + x)) + -66 = 0 0.6((64 + 8x) + x(8 + x)) + -66 = 0 0.6(64 + 8x + (8 * x + x * x)) + -66 = 0 0.6(64 + 8x + (8x + x2)) + -66 = 0 Combine like terms: 8x + 8x = 16x 0.6(64 + 16x + x2) + -66 = 0 (64 * 0.6 + 16x * 0.6 + x2 * 0.6) + -66 = 0 (38.4 + 9.6x + 0.6x2) + -66 = 0 Reorder the terms: 38.4 + -66 + 9.6x + 0.6x2 = 0 Combine like terms: 38.4 + -66 = -27.6 -27.6 + 9.6x + 0.6x2 = 0 Solving -27.6 + 9.6x + 0.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -46 + 16x + x2 = 0 Move the constant term to the right: Add '46' to each side of the equation. -46 + 16x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + 16x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 16x + x2 = 0 + 46 16x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 16x + x2 = 46 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 46 + 64 Reorder the terms: 64 + 16x + x2 = 46 + 64 Combine like terms: 46 + 64 = 110 64 + 16x + x2 = 110 Factor a perfect square on the left side: (x + 8)(x + 8) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (x + 8) equal to 10.488088482 and -10.488088482.Subproblem 1
x + 8 = 10.488088482 Simplifying x + 8 = 10.488088482 Reorder the terms: 8 + x = 10.488088482 Solving 8 + x = 10.488088482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 10.488088482 + -8 Combine like terms: 8 + -8 = 0 0 + x = 10.488088482 + -8 x = 10.488088482 + -8 Combine like terms: 10.488088482 + -8 = 2.488088482 x = 2.488088482 Simplifying x = 2.488088482Subproblem 2
x + 8 = -10.488088482 Simplifying x + 8 = -10.488088482 Reorder the terms: 8 + x = -10.488088482 Solving 8 + x = -10.488088482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -10.488088482 + -8 Combine like terms: 8 + -8 = 0 0 + x = -10.488088482 + -8 x = -10.488088482 + -8 Combine like terms: -10.488088482 + -8 = -18.488088482 x = -18.488088482 Simplifying x = -18.488088482Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.488088482, -18.488088482}
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