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Simplifying 11x = 0.1x2 + -6x + -40 Reorder the terms: 11x = -40 + -6x + 0.1x2 Solving 11x = -40 + -6x + 0.1x2 Solving for variable 'x'. Reorder the terms: 40 + 11x + 6x + -0.1x2 = -40 + -6x + 0.1x2 + 40 + 6x + -0.1x2 Combine like terms: 11x + 6x = 17x 40 + 17x + -0.1x2 = -40 + -6x + 0.1x2 + 40 + 6x + -0.1x2 Reorder the terms: 40 + 17x + -0.1x2 = -40 + 40 + -6x + 6x + 0.1x2 + -0.1x2 Combine like terms: -40 + 40 = 0 40 + 17x + -0.1x2 = 0 + -6x + 6x + 0.1x2 + -0.1x2 40 + 17x + -0.1x2 = -6x + 6x + 0.1x2 + -0.1x2 Combine like terms: -6x + 6x = 0 40 + 17x + -0.1x2 = 0 + 0.1x2 + -0.1x2 40 + 17x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 40 + 17x + -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'. -400 + -170x + x2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -170x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -170x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -170x + x2 = 0 + 400 -170x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -170x + x2 = 400 The x term is -170x. Take half its coefficient (-85). Square it (7225) and add it to both sides. Add '7225' to each side of the equation. -170x + 7225 + x2 = 400 + 7225 Reorder the terms: 7225 + -170x + x2 = 400 + 7225 Combine like terms: 400 + 7225 = 7625 7225 + -170x + x2 = 7625 Factor a perfect square on the left side: (x + -85)(x + -85) = 7625 Calculate the square root of the right side: 87.321245983 Break this problem into two subproblems by setting (x + -85) equal to 87.321245983 and -87.321245983.Subproblem 1
x + -85 = 87.321245983 Simplifying x + -85 = 87.321245983 Reorder the terms: -85 + x = 87.321245983 Solving -85 + x = 87.321245983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + x = 87.321245983 + 85 Combine like terms: -85 + 85 = 0 0 + x = 87.321245983 + 85 x = 87.321245983 + 85 Combine like terms: 87.321245983 + 85 = 172.321245983 x = 172.321245983 Simplifying x = 172.321245983Subproblem 2
x + -85 = -87.321245983 Simplifying x + -85 = -87.321245983 Reorder the terms: -85 + x = -87.321245983 Solving -85 + x = -87.321245983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + x = -87.321245983 + 85 Combine like terms: -85 + 85 = 0 0 + x = -87.321245983 + 85 x = -87.321245983 + 85 Combine like terms: -87.321245983 + 85 = -2.321245983 x = -2.321245983 Simplifying x = -2.321245983Solution
The solution to the problem is based on the solutions from the subproblems. x = {172.321245983, -2.321245983}
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