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Simplifying 31025x2 + 211700x = 55100000 Reorder the terms: 211700x + 31025x2 = 55100000 Solving 211700x + 31025x2 = 55100000 Solving for variable 'x'. Reorder the terms: -55100000 + 211700x + 31025x2 = 55100000 + -55100000 Combine like terms: 55100000 + -55100000 = 0 -55100000 + 211700x + 31025x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(-2204000 + 8468x + 1241x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-2204000 + 8468x + 1241x2)' equal to zero and attempt to solve: Simplifying -2204000 + 8468x + 1241x2 = 0 Solving -2204000 + 8468x + 1241x2 = 0 Begin completing the square. Divide all terms by 1241 the coefficient of the squared term: Divide each side by '1241'. -1775.987107 + 6.823529412x + x2 = 0 Move the constant term to the right: Add '1775.987107' to each side of the equation. -1775.987107 + 6.823529412x + 1775.987107 + x2 = 0 + 1775.987107 Reorder the terms: -1775.987107 + 1775.987107 + 6.823529412x + x2 = 0 + 1775.987107 Combine like terms: -1775.987107 + 1775.987107 = 0.000000 0.000000 + 6.823529412x + x2 = 0 + 1775.987107 6.823529412x + x2 = 0 + 1775.987107 Combine like terms: 0 + 1775.987107 = 1775.987107 6.823529412x + x2 = 1775.987107 The x term is 6.823529412x. Take half its coefficient (3.411764706). Square it (11.64013841) and add it to both sides. Add '11.64013841' to each side of the equation. 6.823529412x + 11.64013841 + x2 = 1775.987107 + 11.64013841 Reorder the terms: 11.64013841 + 6.823529412x + x2 = 1775.987107 + 11.64013841 Combine like terms: 1775.987107 + 11.64013841 = 1787.62724541 11.64013841 + 6.823529412x + x2 = 1787.62724541 Factor a perfect square on the left side: (x + 3.411764706)(x + 3.411764706) = 1787.62724541 Calculate the square root of the right side: 42.280341122 Break this problem into two subproblems by setting (x + 3.411764706) equal to 42.280341122 and -42.280341122.Subproblem 1
x + 3.411764706 = 42.280341122 Simplifying x + 3.411764706 = 42.280341122 Reorder the terms: 3.411764706 + x = 42.280341122 Solving 3.411764706 + x = 42.280341122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.411764706' to each side of the equation. 3.411764706 + -3.411764706 + x = 42.280341122 + -3.411764706 Combine like terms: 3.411764706 + -3.411764706 = 0.000000000 0.000000000 + x = 42.280341122 + -3.411764706 x = 42.280341122 + -3.411764706 Combine like terms: 42.280341122 + -3.411764706 = 38.868576416 x = 38.868576416 Simplifying x = 38.868576416Subproblem 2
x + 3.411764706 = -42.280341122 Simplifying x + 3.411764706 = -42.280341122 Reorder the terms: 3.411764706 + x = -42.280341122 Solving 3.411764706 + x = -42.280341122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.411764706' to each side of the equation. 3.411764706 + -3.411764706 + x = -42.280341122 + -3.411764706 Combine like terms: 3.411764706 + -3.411764706 = 0.000000000 0.000000000 + x = -42.280341122 + -3.411764706 x = -42.280341122 + -3.411764706 Combine like terms: -42.280341122 + -3.411764706 = -45.692105828 x = -45.692105828 Simplifying x = -45.692105828Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.868576416, -45.692105828}Solution
x = {38.868576416, -45.692105828}
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