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Simplifying 10 = 0.1x2 + 4x Reorder the terms: 10 = 4x + 0.1x2 Solving 10 = 4x + 0.1x2 Solving for variable 'x'. Reorder the terms: 10 + -4x + -0.1x2 = 4x + -4x + 0.1x2 + -0.1x2 Combine like terms: 4x + -4x = 0 10 + -4x + -0.1x2 = 0 + 0.1x2 + -0.1x2 10 + -4x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 10 + -4x + -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'. -100 + 40x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 40x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 40x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 40x + x2 = 0 + 100 40x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 40x + x2 = 100 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 100 + 400 Reorder the terms: 400 + 40x + x2 = 100 + 400 Combine like terms: 100 + 400 = 500 400 + 40x + x2 = 500 Factor a perfect square on the left side: (x + 20)(x + 20) = 500 Calculate the square root of the right side: 22.360679775 Break this problem into two subproblems by setting (x + 20) equal to 22.360679775 and -22.360679775.Subproblem 1
x + 20 = 22.360679775 Simplifying x + 20 = 22.360679775 Reorder the terms: 20 + x = 22.360679775 Solving 20 + x = 22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 22.360679775 + -20 Combine like terms: 20 + -20 = 0 0 + x = 22.360679775 + -20 x = 22.360679775 + -20 Combine like terms: 22.360679775 + -20 = 2.360679775 x = 2.360679775 Simplifying x = 2.360679775Subproblem 2
x + 20 = -22.360679775 Simplifying x + 20 = -22.360679775 Reorder the terms: 20 + x = -22.360679775 Solving 20 + x = -22.360679775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -22.360679775 + -20 Combine like terms: 20 + -20 = 0 0 + x = -22.360679775 + -20 x = -22.360679775 + -20 Combine like terms: -22.360679775 + -20 = -42.360679775 x = -42.360679775 Simplifying x = -42.360679775Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.360679775, -42.360679775}
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