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Simplifying 2x2 + -29x + 7 = 0 Reorder the terms: 7 + -29x + 2x2 = 0 Solving 7 + -29x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -14.5x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -14.5x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -14.5x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -14.5x + x2 = 0 + -3.5 -14.5x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -14.5x + x2 = -3.5 The x term is -14.5x. Take half its coefficient (-7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. -14.5x + 52.5625 + x2 = -3.5 + 52.5625 Reorder the terms: 52.5625 + -14.5x + x2 = -3.5 + 52.5625 Combine like terms: -3.5 + 52.5625 = 49.0625 52.5625 + -14.5x + x2 = 49.0625 Factor a perfect square on the left side: (x + -7.25)(x + -7.25) = 49.0625 Calculate the square root of the right side: 7.004462863 Break this problem into two subproblems by setting (x + -7.25) equal to 7.004462863 and -7.004462863.Subproblem 1
x + -7.25 = 7.004462863 Simplifying x + -7.25 = 7.004462863 Reorder the terms: -7.25 + x = 7.004462863 Solving -7.25 + x = 7.004462863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = 7.004462863 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 7.004462863 + 7.25 x = 7.004462863 + 7.25 Combine like terms: 7.004462863 + 7.25 = 14.254462863 x = 14.254462863 Simplifying x = 14.254462863Subproblem 2
x + -7.25 = -7.004462863 Simplifying x + -7.25 = -7.004462863 Reorder the terms: -7.25 + x = -7.004462863 Solving -7.25 + x = -7.004462863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = -7.004462863 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -7.004462863 + 7.25 x = -7.004462863 + 7.25 Combine like terms: -7.004462863 + 7.25 = 0.245537137 x = 0.245537137 Simplifying x = 0.245537137Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.254462863, 0.245537137}
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