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Simplifying 45.5x2 + -160x + 90 = 0 Reorder the terms: 90 + -160x + 45.5x2 = 0 Solving 90 + -160x + 45.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45.5 the coefficient of the squared term: Divide each side by '45.5'. 1.978021978 + -3.516483516x + x2 = 0 Move the constant term to the right: Add '-1.978021978' to each side of the equation. 1.978021978 + -3.516483516x + -1.978021978 + x2 = 0 + -1.978021978 Reorder the terms: 1.978021978 + -1.978021978 + -3.516483516x + x2 = 0 + -1.978021978 Combine like terms: 1.978021978 + -1.978021978 = 0.000000000 0.000000000 + -3.516483516x + x2 = 0 + -1.978021978 -3.516483516x + x2 = 0 + -1.978021978 Combine like terms: 0 + -1.978021978 = -1.978021978 -3.516483516x + x2 = -1.978021978 The x term is -3.516483516x. Take half its coefficient (-1.758241758). Square it (3.091414080) and add it to both sides. Add '3.091414080' to each side of the equation. -3.516483516x + 3.091414080 + x2 = -1.978021978 + 3.091414080 Reorder the terms: 3.091414080 + -3.516483516x + x2 = -1.978021978 + 3.091414080 Combine like terms: -1.978021978 + 3.091414080 = 1.113392102 3.091414080 + -3.516483516x + x2 = 1.113392102 Factor a perfect square on the left side: (x + -1.758241758)(x + -1.758241758) = 1.113392102 Calculate the square root of the right side: 1.055173968 Break this problem into two subproblems by setting (x + -1.758241758) equal to 1.055173968 and -1.055173968.Subproblem 1
x + -1.758241758 = 1.055173968 Simplifying x + -1.758241758 = 1.055173968 Reorder the terms: -1.758241758 + x = 1.055173968 Solving -1.758241758 + x = 1.055173968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.758241758' to each side of the equation. -1.758241758 + 1.758241758 + x = 1.055173968 + 1.758241758 Combine like terms: -1.758241758 + 1.758241758 = 0.000000000 0.000000000 + x = 1.055173968 + 1.758241758 x = 1.055173968 + 1.758241758 Combine like terms: 1.055173968 + 1.758241758 = 2.813415726 x = 2.813415726 Simplifying x = 2.813415726Subproblem 2
x + -1.758241758 = -1.055173968 Simplifying x + -1.758241758 = -1.055173968 Reorder the terms: -1.758241758 + x = -1.055173968 Solving -1.758241758 + x = -1.055173968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.758241758' to each side of the equation. -1.758241758 + 1.758241758 + x = -1.055173968 + 1.758241758 Combine like terms: -1.758241758 + 1.758241758 = 0.000000000 0.000000000 + x = -1.055173968 + 1.758241758 x = -1.055173968 + 1.758241758 Combine like terms: -1.055173968 + 1.758241758 = 0.70306779 x = 0.70306779 Simplifying x = 0.70306779Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.813415726, 0.70306779}
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