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Simplifying 100x2 + -29x + -125 = 0 Reorder the terms: -125 + -29x + 100x2 = 0 Solving -125 + -29x + 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 + -0.29x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -0.29x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -0.29x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.29x + x2 = 0 + 1.25 -0.29x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -0.29x + x2 = 1.25 The x term is -0.29x. Take half its coefficient (-0.145). Square it (0.021025) and add it to both sides. Add '0.021025' to each side of the equation. -0.29x + 0.021025 + x2 = 1.25 + 0.021025 Reorder the terms: 0.021025 + -0.29x + x2 = 1.25 + 0.021025 Combine like terms: 1.25 + 0.021025 = 1.271025 0.021025 + -0.29x + x2 = 1.271025 Factor a perfect square on the left side: (x + -0.145)(x + -0.145) = 1.271025 Calculate the square root of the right side: 1.127397445 Break this problem into two subproblems by setting (x + -0.145) equal to 1.127397445 and -1.127397445.Subproblem 1
x + -0.145 = 1.127397445 Simplifying x + -0.145 = 1.127397445 Reorder the terms: -0.145 + x = 1.127397445 Solving -0.145 + x = 1.127397445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.145' to each side of the equation. -0.145 + 0.145 + x = 1.127397445 + 0.145 Combine like terms: -0.145 + 0.145 = 0.000 0.000 + x = 1.127397445 + 0.145 x = 1.127397445 + 0.145 Combine like terms: 1.127397445 + 0.145 = 1.272397445 x = 1.272397445 Simplifying x = 1.272397445Subproblem 2
x + -0.145 = -1.127397445 Simplifying x + -0.145 = -1.127397445 Reorder the terms: -0.145 + x = -1.127397445 Solving -0.145 + x = -1.127397445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.145' to each side of the equation. -0.145 + 0.145 + x = -1.127397445 + 0.145 Combine like terms: -0.145 + 0.145 = 0.000 0.000 + x = -1.127397445 + 0.145 x = -1.127397445 + 0.145 Combine like terms: -1.127397445 + 0.145 = -0.982397445 x = -0.982397445 Simplifying x = -0.982397445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.272397445, -0.982397445}
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