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Simplifying -0.22x2 + 23x + -251 = 0 Reorder the terms: -251 + 23x + -0.22x2 = 0 Solving -251 + 23x + -0.22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.22 the coefficient of the squared term: Divide each side by '-0.22'. 1140.909091 + -104.5454545x + x2 = 0 Move the constant term to the right: Add '-1140.909091' to each side of the equation. 1140.909091 + -104.5454545x + -1140.909091 + x2 = 0 + -1140.909091 Reorder the terms: 1140.909091 + -1140.909091 + -104.5454545x + x2 = 0 + -1140.909091 Combine like terms: 1140.909091 + -1140.909091 = 0.000000 0.000000 + -104.5454545x + x2 = 0 + -1140.909091 -104.5454545x + x2 = 0 + -1140.909091 Combine like terms: 0 + -1140.909091 = -1140.909091 -104.5454545x + x2 = -1140.909091 The x term is -104.5454545x. Take half its coefficient (-52.27272725). Square it (2732.438014) and add it to both sides. Add '2732.438014' to each side of the equation. -104.5454545x + 2732.438014 + x2 = -1140.909091 + 2732.438014 Reorder the terms: 2732.438014 + -104.5454545x + x2 = -1140.909091 + 2732.438014 Combine like terms: -1140.909091 + 2732.438014 = 1591.528923 2732.438014 + -104.5454545x + x2 = 1591.528923 Factor a perfect square on the left side: (x + -52.27272725)(x + -52.27272725) = 1591.528923 Calculate the square root of the right side: 39.893971011 Break this problem into two subproblems by setting (x + -52.27272725) equal to 39.893971011 and -39.893971011.Subproblem 1
x + -52.27272725 = 39.893971011 Simplifying x + -52.27272725 = 39.893971011 Reorder the terms: -52.27272725 + x = 39.893971011 Solving -52.27272725 + x = 39.893971011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.27272725' to each side of the equation. -52.27272725 + 52.27272725 + x = 39.893971011 + 52.27272725 Combine like terms: -52.27272725 + 52.27272725 = 0.00000000 0.00000000 + x = 39.893971011 + 52.27272725 x = 39.893971011 + 52.27272725 Combine like terms: 39.893971011 + 52.27272725 = 92.166698261 x = 92.166698261 Simplifying x = 92.166698261Subproblem 2
x + -52.27272725 = -39.893971011 Simplifying x + -52.27272725 = -39.893971011 Reorder the terms: -52.27272725 + x = -39.893971011 Solving -52.27272725 + x = -39.893971011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.27272725' to each side of the equation. -52.27272725 + 52.27272725 + x = -39.893971011 + 52.27272725 Combine like terms: -52.27272725 + 52.27272725 = 0.00000000 0.00000000 + x = -39.893971011 + 52.27272725 x = -39.893971011 + 52.27272725 Combine like terms: -39.893971011 + 52.27272725 = 12.378756239 x = 12.378756239 Simplifying x = 12.378756239Solution
The solution to the problem is based on the solutions from the subproblems. x = {92.166698261, 12.378756239}
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