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Simplifying 0 = x(5x + 0.5) + -168 Reorder the terms: 0 = x(0.5 + 5x) + -168 0 = (0.5 * x + 5x * x) + -168 0 = (0.5x + 5x2) + -168 Reorder the terms: 0 = -168 + 0.5x + 5x2 Solving 0 = -168 + 0.5x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 168 = 168 168 + -0.5x + -5x2 = -168 + 0.5x + 5x2 + 168 + -0.5x + -5x2 Reorder the terms: 168 + -0.5x + -5x2 = -168 + 168 + 0.5x + -0.5x + 5x2 + -5x2 Combine like terms: -168 + 168 = 0 168 + -0.5x + -5x2 = 0 + 0.5x + -0.5x + 5x2 + -5x2 168 + -0.5x + -5x2 = 0.5x + -0.5x + 5x2 + -5x2 Combine like terms: 0.5x + -0.5x = 0.0 168 + -0.5x + -5x2 = 0.0 + 5x2 + -5x2 168 + -0.5x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 168 + -0.5x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -33.6 + 0.1x + x2 = 0 Move the constant term to the right: Add '33.6' to each side of the equation. -33.6 + 0.1x + 33.6 + x2 = 0 + 33.6 Reorder the terms: -33.6 + 33.6 + 0.1x + x2 = 0 + 33.6 Combine like terms: -33.6 + 33.6 = 0.0 0.0 + 0.1x + x2 = 0 + 33.6 0.1x + x2 = 0 + 33.6 Combine like terms: 0 + 33.6 = 33.6 0.1x + x2 = 33.6 The x term is 0.1x. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1x + 0.0025 + x2 = 33.6 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 33.6 + 0.0025 Combine like terms: 33.6 + 0.0025 = 33.6025 0.0025 + 0.1x + x2 = 33.6025 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 33.6025 Calculate the square root of the right side: 5.79676634 Break this problem into two subproblems by setting (x + 0.05) equal to 5.79676634 and -5.79676634.Subproblem 1
x + 0.05 = 5.79676634 Simplifying x + 0.05 = 5.79676634 Reorder the terms: 0.05 + x = 5.79676634 Solving 0.05 + x = 5.79676634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 5.79676634 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 5.79676634 + -0.05 x = 5.79676634 + -0.05 Combine like terms: 5.79676634 + -0.05 = 5.74676634 x = 5.74676634 Simplifying x = 5.74676634Subproblem 2
x + 0.05 = -5.79676634 Simplifying x + 0.05 = -5.79676634 Reorder the terms: 0.05 + x = -5.79676634 Solving 0.05 + x = -5.79676634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -5.79676634 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -5.79676634 + -0.05 x = -5.79676634 + -0.05 Combine like terms: -5.79676634 + -0.05 = -5.84676634 x = -5.84676634 Simplifying x = -5.84676634Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.74676634, -5.84676634}
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