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Simplifying 8 = 10 + -0.05x + -1(0.1x2) Remove parenthesis around (0.1x2) 8 = 10 + -0.05x + -1 * 0.1x2 Multiply -1 * 0.1 8 = 10 + -0.05x + -0.1x2 Solving 8 = 10 + -0.05x + -0.1x2 Solving for variable 'x'. Combine like terms: 8 + -10 = -2 -2 + 0.05x + 0.1x2 = 10 + -0.05x + -0.1x2 + -10 + 0.05x + 0.1x2 Reorder the terms: -2 + 0.05x + 0.1x2 = 10 + -10 + -0.05x + 0.05x + -0.1x2 + 0.1x2 Combine like terms: 10 + -10 = 0 -2 + 0.05x + 0.1x2 = 0 + -0.05x + 0.05x + -0.1x2 + 0.1x2 -2 + 0.05x + 0.1x2 = -0.05x + 0.05x + -0.1x2 + 0.1x2 Combine like terms: -0.05x + 0.05x = 0.00 -2 + 0.05x + 0.1x2 = 0.00 + -0.1x2 + 0.1x2 -2 + 0.05x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 -2 + 0.05x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -20 + 0.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 0.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 0.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 0.5x + x2 = 0 + 20 0.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 0.5x + x2 = 20 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 20 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 20 + 0.0625 Combine like terms: 20 + 0.0625 = 20.0625 0.0625 + 0.5x + x2 = 20.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (x + 0.25) equal to 4.479118217 and -4.479118217.Subproblem 1
x + 0.25 = 4.479118217 Simplifying x + 0.25 = 4.479118217 Reorder the terms: 0.25 + x = 4.479118217 Solving 0.25 + x = 4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 4.479118217 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.479118217 + -0.25 x = 4.479118217 + -0.25 Combine like terms: 4.479118217 + -0.25 = 4.229118217 x = 4.229118217 Simplifying x = 4.229118217Subproblem 2
x + 0.25 = -4.479118217 Simplifying x + 0.25 = -4.479118217 Reorder the terms: 0.25 + x = -4.479118217 Solving 0.25 + x = -4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -4.479118217 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.479118217 + -0.25 x = -4.479118217 + -0.25 Combine like terms: -4.479118217 + -0.25 = -4.729118217 x = -4.729118217 Simplifying x = -4.729118217Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.229118217, -4.729118217}
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