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Simplifying 152.41 + -250.52x + 99x2 = 0 Solving 152.41 + -250.52x + 99x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 99 the coefficient of the squared term: Divide each side by '99'. 1.539494949 + -2.530505051x + x2 = 0 Move the constant term to the right: Add '-1.539494949' to each side of the equation. 1.539494949 + -2.530505051x + -1.539494949 + x2 = 0 + -1.539494949 Reorder the terms: 1.539494949 + -1.539494949 + -2.530505051x + x2 = 0 + -1.539494949 Combine like terms: 1.539494949 + -1.539494949 = 0.000000000 0.000000000 + -2.530505051x + x2 = 0 + -1.539494949 -2.530505051x + x2 = 0 + -1.539494949 Combine like terms: 0 + -1.539494949 = -1.539494949 -2.530505051x + x2 = -1.539494949 The x term is -2.530505051x. Take half its coefficient (-1.265252526). Square it (1.600863955) and add it to both sides. Add '1.600863955' to each side of the equation. -2.530505051x + 1.600863955 + x2 = -1.539494949 + 1.600863955 Reorder the terms: 1.600863955 + -2.530505051x + x2 = -1.539494949 + 1.600863955 Combine like terms: -1.539494949 + 1.600863955 = 0.061369006 1.600863955 + -2.530505051x + x2 = 0.061369006 Factor a perfect square on the left side: (x + -1.265252526)(x + -1.265252526) = 0.061369006 Calculate the square root of the right side: 0.247727685 Break this problem into two subproblems by setting (x + -1.265252526) equal to 0.247727685 and -0.247727685.Subproblem 1
x + -1.265252526 = 0.247727685 Simplifying x + -1.265252526 = 0.247727685 Reorder the terms: -1.265252526 + x = 0.247727685 Solving -1.265252526 + x = 0.247727685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.265252526' to each side of the equation. -1.265252526 + 1.265252526 + x = 0.247727685 + 1.265252526 Combine like terms: -1.265252526 + 1.265252526 = 0.000000000 0.000000000 + x = 0.247727685 + 1.265252526 x = 0.247727685 + 1.265252526 Combine like terms: 0.247727685 + 1.265252526 = 1.512980211 x = 1.512980211 Simplifying x = 1.512980211Subproblem 2
x + -1.265252526 = -0.247727685 Simplifying x + -1.265252526 = -0.247727685 Reorder the terms: -1.265252526 + x = -0.247727685 Solving -1.265252526 + x = -0.247727685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.265252526' to each side of the equation. -1.265252526 + 1.265252526 + x = -0.247727685 + 1.265252526 Combine like terms: -1.265252526 + 1.265252526 = 0.000000000 0.000000000 + x = -0.247727685 + 1.265252526 x = -0.247727685 + 1.265252526 Combine like terms: -0.247727685 + 1.265252526 = 1.017524841 x = 1.017524841 Simplifying x = 1.017524841Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.512980211, 1.017524841}
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