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Simplifying 2x2 + -4x = 207.113592 Reorder the terms: -4x + 2x2 = 207.113592 Solving -4x + 2x2 = 207.113592 Solving for variable 'x'. Reorder the terms: -207.113592 + -4x + 2x2 = 207.113592 + -207.113592 Combine like terms: 207.113592 + -207.113592 = 0.000000 -207.113592 + -4x + 2x2 = 0.000000 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -103.556796 + -2x + x2 = 0.000000 Move the constant term to the right: Add '103.556796' to each side of the equation. -103.556796 + -2x + 103.556796 + x2 = 0.000000 + 103.556796 Reorder the terms: -103.556796 + 103.556796 + -2x + x2 = 0.000000 + 103.556796 Combine like terms: -103.556796 + 103.556796 = 0.000000 0.000000 + -2x + x2 = 0.000000 + 103.556796 -2x + x2 = 0.000000 + 103.556796 Combine like terms: 0.000000 + 103.556796 = 103.556796 -2x + x2 = 103.556796 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 103.556796 + 1 Reorder the terms: 1 + -2x + x2 = 103.556796 + 1 Combine like terms: 103.556796 + 1 = 104.556796 1 + -2x + x2 = 104.556796 Factor a perfect square on the left side: (x + -1)(x + -1) = 104.556796 Calculate the square root of the right side: 10.225301756 Break this problem into two subproblems by setting (x + -1) equal to 10.225301756 and -10.225301756.Subproblem 1
x + -1 = 10.225301756 Simplifying x + -1 = 10.225301756 Reorder the terms: -1 + x = 10.225301756 Solving -1 + x = 10.225301756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 10.225301756 + 1 Combine like terms: -1 + 1 = 0 0 + x = 10.225301756 + 1 x = 10.225301756 + 1 Combine like terms: 10.225301756 + 1 = 11.225301756 x = 11.225301756 Simplifying x = 11.225301756Subproblem 2
x + -1 = -10.225301756 Simplifying x + -1 = -10.225301756 Reorder the terms: -1 + x = -10.225301756 Solving -1 + x = -10.225301756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -10.225301756 + 1 Combine like terms: -1 + 1 = 0 0 + x = -10.225301756 + 1 x = -10.225301756 + 1 Combine like terms: -10.225301756 + 1 = -9.225301756 x = -9.225301756 Simplifying x = -9.225301756Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.225301756, -9.225301756}
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