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Simplifying 100x2 + -149x + -125 = 0 Reorder the terms: -125 + -149x + 100x2 = 0 Solving -125 + -149x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -1.25 + -1.49x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -1.49x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -1.49x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -1.49x + x2 = 0 + 1.25 -1.49x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -1.49x + x2 = 1.25 The x term is -1.49x. Take half its coefficient (-0.745). Square it (0.555025) and add it to both sides. Add '0.555025' to each side of the equation. -1.49x + 0.555025 + x2 = 1.25 + 0.555025 Reorder the terms: 0.555025 + -1.49x + x2 = 1.25 + 0.555025 Combine like terms: 1.25 + 0.555025 = 1.805025 0.555025 + -1.49x + x2 = 1.805025 Factor a perfect square on the left side: (x + -0.745)(x + -0.745) = 1.805025 Calculate the square root of the right side: 1.343512188 Break this problem into two subproblems by setting (x + -0.745) equal to 1.343512188 and -1.343512188.Subproblem 1
x + -0.745 = 1.343512188 Simplifying x + -0.745 = 1.343512188 Reorder the terms: -0.745 + x = 1.343512188 Solving -0.745 + x = 1.343512188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.745' to each side of the equation. -0.745 + 0.745 + x = 1.343512188 + 0.745 Combine like terms: -0.745 + 0.745 = 0.000 0.000 + x = 1.343512188 + 0.745 x = 1.343512188 + 0.745 Combine like terms: 1.343512188 + 0.745 = 2.088512188 x = 2.088512188 Simplifying x = 2.088512188Subproblem 2
x + -0.745 = -1.343512188 Simplifying x + -0.745 = -1.343512188 Reorder the terms: -0.745 + x = -1.343512188 Solving -0.745 + x = -1.343512188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.745' to each side of the equation. -0.745 + 0.745 + x = -1.343512188 + 0.745 Combine like terms: -0.745 + 0.745 = 0.000 0.000 + x = -1.343512188 + 0.745 x = -1.343512188 + 0.745 Combine like terms: -1.343512188 + 0.745 = -0.598512188 x = -0.598512188 Simplifying x = -0.598512188Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.088512188, -0.598512188}
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