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Simplifying 4.9x2 + 340x + -1088 = 0 Reorder the terms: -1088 + 340x + 4.9x2 = 0 Solving -1088 + 340x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -222.0408163 + 69.3877551x + x2 = 0 Move the constant term to the right: Add '222.0408163' to each side of the equation. -222.0408163 + 69.3877551x + 222.0408163 + x2 = 0 + 222.0408163 Reorder the terms: -222.0408163 + 222.0408163 + 69.3877551x + x2 = 0 + 222.0408163 Combine like terms: -222.0408163 + 222.0408163 = 0.0000000 0.0000000 + 69.3877551x + x2 = 0 + 222.0408163 69.3877551x + x2 = 0 + 222.0408163 Combine like terms: 0 + 222.0408163 = 222.0408163 69.3877551x + x2 = 222.0408163 The x term is 69.3877551x. Take half its coefficient (34.69387755). Square it (1203.665139) and add it to both sides. Add '1203.665139' to each side of the equation. 69.3877551x + 1203.665139 + x2 = 222.0408163 + 1203.665139 Reorder the terms: 1203.665139 + 69.3877551x + x2 = 222.0408163 + 1203.665139 Combine like terms: 222.0408163 + 1203.665139 = 1425.7059553 1203.665139 + 69.3877551x + x2 = 1425.7059553 Factor a perfect square on the left side: (x + 34.69387755)(x + 34.69387755) = 1425.7059553 Calculate the square root of the right side: 37.758521625 Break this problem into two subproblems by setting (x + 34.69387755) equal to 37.758521625 and -37.758521625.Subproblem 1
x + 34.69387755 = 37.758521625 Simplifying x + 34.69387755 = 37.758521625 Reorder the terms: 34.69387755 + x = 37.758521625 Solving 34.69387755 + x = 37.758521625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.69387755' to each side of the equation. 34.69387755 + -34.69387755 + x = 37.758521625 + -34.69387755 Combine like terms: 34.69387755 + -34.69387755 = 0.00000000 0.00000000 + x = 37.758521625 + -34.69387755 x = 37.758521625 + -34.69387755 Combine like terms: 37.758521625 + -34.69387755 = 3.064644075 x = 3.064644075 Simplifying x = 3.064644075Subproblem 2
x + 34.69387755 = -37.758521625 Simplifying x + 34.69387755 = -37.758521625 Reorder the terms: 34.69387755 + x = -37.758521625 Solving 34.69387755 + x = -37.758521625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.69387755' to each side of the equation. 34.69387755 + -34.69387755 + x = -37.758521625 + -34.69387755 Combine like terms: 34.69387755 + -34.69387755 = 0.00000000 0.00000000 + x = -37.758521625 + -34.69387755 x = -37.758521625 + -34.69387755 Combine like terms: -37.758521625 + -34.69387755 = -72.452399175 x = -72.452399175 Simplifying x = -72.452399175Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.064644075, -72.452399175}
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