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Simplifying 120 = 0.05x2 + 1.1x Reorder the terms: 120 = 1.1x + 0.05x2 Solving 120 = 1.1x + 0.05x2 Solving for variable 'x'. Reorder the terms: 120 + -1.1x + -0.05x2 = 1.1x + -1.1x + 0.05x2 + -0.05x2 Combine like terms: 1.1x + -1.1x = 0.0 120 + -1.1x + -0.05x2 = 0.0 + 0.05x2 + -0.05x2 120 + -1.1x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 120 + -1.1x + -0.05x2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -2400 + 22x + x2 = 0 Move the constant term to the right: Add '2400' to each side of the equation. -2400 + 22x + 2400 + x2 = 0 + 2400 Reorder the terms: -2400 + 2400 + 22x + x2 = 0 + 2400 Combine like terms: -2400 + 2400 = 0 0 + 22x + x2 = 0 + 2400 22x + x2 = 0 + 2400 Combine like terms: 0 + 2400 = 2400 22x + x2 = 2400 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 2400 + 121 Reorder the terms: 121 + 22x + x2 = 2400 + 121 Combine like terms: 2400 + 121 = 2521 121 + 22x + x2 = 2521 Factor a perfect square on the left side: (x + 11)(x + 11) = 2521 Calculate the square root of the right side: 50.209560843 Break this problem into two subproblems by setting (x + 11) equal to 50.209560843 and -50.209560843.Subproblem 1
x + 11 = 50.209560843 Simplifying x + 11 = 50.209560843 Reorder the terms: 11 + x = 50.209560843 Solving 11 + x = 50.209560843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 50.209560843 + -11 Combine like terms: 11 + -11 = 0 0 + x = 50.209560843 + -11 x = 50.209560843 + -11 Combine like terms: 50.209560843 + -11 = 39.209560843 x = 39.209560843 Simplifying x = 39.209560843Subproblem 2
x + 11 = -50.209560843 Simplifying x + 11 = -50.209560843 Reorder the terms: 11 + x = -50.209560843 Solving 11 + x = -50.209560843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -50.209560843 + -11 Combine like terms: 11 + -11 = 0 0 + x = -50.209560843 + -11 x = -50.209560843 + -11 Combine like terms: -50.209560843 + -11 = -61.209560843 x = -61.209560843 Simplifying x = -61.209560843Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.209560843, -61.209560843}
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