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Simplifying 0.6x(x + 10) = 86 Reorder the terms: 0.6x(10 + x) = 86 (10 * 0.6x + x * 0.6x) = 86 (6x + 0.6x2) = 86 Solving 6x + 0.6x2 = 86 Solving for variable 'x'. Reorder the terms: -86 + 6x + 0.6x2 = 86 + -86 Combine like terms: 86 + -86 = 0 -86 + 6x + 0.6x2 = 0 Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -143.3333333 + 10x + x2 = 0 Move the constant term to the right: Add '143.3333333' to each side of the equation. -143.3333333 + 10x + 143.3333333 + x2 = 0 + 143.3333333 Reorder the terms: -143.3333333 + 143.3333333 + 10x + x2 = 0 + 143.3333333 Combine like terms: -143.3333333 + 143.3333333 = 0.0000000 0.0000000 + 10x + x2 = 0 + 143.3333333 10x + x2 = 0 + 143.3333333 Combine like terms: 0 + 143.3333333 = 143.3333333 10x + x2 = 143.3333333 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 143.3333333 + 25 Reorder the terms: 25 + 10x + x2 = 143.3333333 + 25 Combine like terms: 143.3333333 + 25 = 168.3333333 25 + 10x + x2 = 168.3333333 Factor a perfect square on the left side: (x + 5)(x + 5) = 168.3333333 Calculate the square root of the right side: 12.974333636 Break this problem into two subproblems by setting (x + 5) equal to 12.974333636 and -12.974333636.Subproblem 1
x + 5 = 12.974333636 Simplifying x + 5 = 12.974333636 Reorder the terms: 5 + x = 12.974333636 Solving 5 + x = 12.974333636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 12.974333636 + -5 Combine like terms: 5 + -5 = 0 0 + x = 12.974333636 + -5 x = 12.974333636 + -5 Combine like terms: 12.974333636 + -5 = 7.974333636 x = 7.974333636 Simplifying x = 7.974333636Subproblem 2
x + 5 = -12.974333636 Simplifying x + 5 = -12.974333636 Reorder the terms: 5 + x = -12.974333636 Solving 5 + x = -12.974333636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -12.974333636 + -5 Combine like terms: 5 + -5 = 0 0 + x = -12.974333636 + -5 x = -12.974333636 + -5 Combine like terms: -12.974333636 + -5 = -17.974333636 x = -17.974333636 Simplifying x = -17.974333636Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.974333636, -17.974333636}
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