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Simplifying -125 + 1.1x + 0.05x2 = 0 Solving -125 + 1.1x + 0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -2500 + 22x + x2 = 0 Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 22x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 22x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 22x + x2 = 0 + 2500 22x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 22x + x2 = 2500 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 = 2500 + 121 Reorder the terms: 121 + 22x + x2 = 2500 + 121 Combine like terms: 2500 + 121 = 2621 121 + 22x + x2 = 2621 Factor a perfect square on the left side: (x + 11)(x + 11) = 2621 Calculate the square root of the right side: 51.195702945 Break this problem into two subproblems by setting (x + 11) equal to 51.195702945 and -51.195702945.Subproblem 1
x + 11 = 51.195702945 Simplifying x + 11 = 51.195702945 Reorder the terms: 11 + x = 51.195702945 Solving 11 + x = 51.195702945 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 = 51.195702945 + -11 Combine like terms: 11 + -11 = 0 0 + x = 51.195702945 + -11 x = 51.195702945 + -11 Combine like terms: 51.195702945 + -11 = 40.195702945 x = 40.195702945 Simplifying x = 40.195702945Subproblem 2
x + 11 = -51.195702945 Simplifying x + 11 = -51.195702945 Reorder the terms: 11 + x = -51.195702945 Solving 11 + x = -51.195702945 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 = -51.195702945 + -11 Combine like terms: 11 + -11 = 0 0 + x = -51.195702945 + -11 x = -51.195702945 + -11 Combine like terms: -51.195702945 + -11 = -62.195702945 x = -62.195702945 Simplifying x = -62.195702945Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.195702945, -62.195702945}
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