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Simplifying 0 = 2x2 + -29x + 30 Reorder the terms: 0 = 30 + -29x + 2x2 Solving 0 = 30 + -29x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -30 = -30 -30 + 29x + -2x2 = 30 + -29x + 2x2 + -30 + 29x + -2x2 Reorder the terms: -30 + 29x + -2x2 = 30 + -30 + -29x + 29x + 2x2 + -2x2 Combine like terms: 30 + -30 = 0 -30 + 29x + -2x2 = 0 + -29x + 29x + 2x2 + -2x2 -30 + 29x + -2x2 = -29x + 29x + 2x2 + -2x2 Combine like terms: -29x + 29x = 0 -30 + 29x + -2x2 = 0 + 2x2 + -2x2 -30 + 29x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -30 + 29x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 15 + -14.5x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -14.5x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -14.5x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -14.5x + x2 = 0 + -15 -14.5x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -14.5x + x2 = -15 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 = -15 + 52.5625 Reorder the terms: 52.5625 + -14.5x + x2 = -15 + 52.5625 Combine like terms: -15 + 52.5625 = 37.5625 52.5625 + -14.5x + x2 = 37.5625 Factor a perfect square on the left side: (x + -7.25)(x + -7.25) = 37.5625 Calculate the square root of the right side: 6.128825336 Break this problem into two subproblems by setting (x + -7.25) equal to 6.128825336 and -6.128825336.Subproblem 1
x + -7.25 = 6.128825336 Simplifying x + -7.25 = 6.128825336 Reorder the terms: -7.25 + x = 6.128825336 Solving -7.25 + x = 6.128825336 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 = 6.128825336 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 6.128825336 + 7.25 x = 6.128825336 + 7.25 Combine like terms: 6.128825336 + 7.25 = 13.378825336 x = 13.378825336 Simplifying x = 13.378825336Subproblem 2
x + -7.25 = -6.128825336 Simplifying x + -7.25 = -6.128825336 Reorder the terms: -7.25 + x = -6.128825336 Solving -7.25 + x = -6.128825336 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 = -6.128825336 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -6.128825336 + 7.25 x = -6.128825336 + 7.25 Combine like terms: -6.128825336 + 7.25 = 1.121174664 x = 1.121174664 Simplifying x = 1.121174664Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.378825336, 1.121174664}
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