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Simplifying 5x[2(x + -10) + 3] = 8 Reorder the terms: 5x[2(-10 + x) + 3] = 8 5x[(-10 * 2 + x * 2) + 3] = 8 5x[(-20 + 2x) + 3] = 8 Reorder the terms: 5x[-20 + 3 + 2x] = 8 Combine like terms: -20 + 3 = -17 5x[-17 + 2x] = 8 [-17 * 5x + 2x * 5x] = 8 [-85x + 10x2] = 8 Solving -85x + 10x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -85x + 10x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -85x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.8 + -8.5x + x2 = 0.0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -8.5x + 0.8 + x2 = 0.0 + 0.8 Reorder the terms: -0.8 + 0.8 + -8.5x + x2 = 0.0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -8.5x + x2 = 0.0 + 0.8 -8.5x + x2 = 0.0 + 0.8 Combine like terms: 0.0 + 0.8 = 0.8 -8.5x + x2 = 0.8 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 0.8 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 0.8 + 18.0625 Combine like terms: 0.8 + 18.0625 = 18.8625 18.0625 + -8.5x + x2 = 18.8625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 18.8625 Calculate the square root of the right side: 4.343097973 Break this problem into two subproblems by setting (x + -4.25) equal to 4.343097973 and -4.343097973.Subproblem 1
x + -4.25 = 4.343097973 Simplifying x + -4.25 = 4.343097973 Reorder the terms: -4.25 + x = 4.343097973 Solving -4.25 + x = 4.343097973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.343097973 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.343097973 + 4.25 x = 4.343097973 + 4.25 Combine like terms: 4.343097973 + 4.25 = 8.593097973 x = 8.593097973 Simplifying x = 8.593097973Subproblem 2
x + -4.25 = -4.343097973 Simplifying x + -4.25 = -4.343097973 Reorder the terms: -4.25 + x = -4.343097973 Solving -4.25 + x = -4.343097973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.343097973 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.343097973 + 4.25 x = -4.343097973 + 4.25 Combine like terms: -4.343097973 + 4.25 = -0.093097973 x = -0.093097973 Simplifying x = -0.093097973Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.593097973, -0.093097973}
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