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Simplifying 2x2 + 4x = 205 Reorder the terms: 4x + 2x2 = 205 Solving 4x + 2x2 = 205 Solving for variable 'x'. Reorder the terms: -205 + 4x + 2x2 = 205 + -205 Combine like terms: 205 + -205 = 0 -205 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -102.5 + 2x + x2 = 0 Move the constant term to the right: Add '102.5' to each side of the equation. -102.5 + 2x + 102.5 + x2 = 0 + 102.5 Reorder the terms: -102.5 + 102.5 + 2x + x2 = 0 + 102.5 Combine like terms: -102.5 + 102.5 = 0.0 0.0 + 2x + x2 = 0 + 102.5 2x + x2 = 0 + 102.5 Combine like terms: 0 + 102.5 = 102.5 2x + x2 = 102.5 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 = 102.5 + 1 Reorder the terms: 1 + 2x + x2 = 102.5 + 1 Combine like terms: 102.5 + 1 = 103.5 1 + 2x + x2 = 103.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 103.5 Calculate the square root of the right side: 10.173494975 Break this problem into two subproblems by setting (x + 1) equal to 10.173494975 and -10.173494975.Subproblem 1
x + 1 = 10.173494975 Simplifying x + 1 = 10.173494975 Reorder the terms: 1 + x = 10.173494975 Solving 1 + x = 10.173494975 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 = 10.173494975 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.173494975 + -1 x = 10.173494975 + -1 Combine like terms: 10.173494975 + -1 = 9.173494975 x = 9.173494975 Simplifying x = 9.173494975Subproblem 2
x + 1 = -10.173494975 Simplifying x + 1 = -10.173494975 Reorder the terms: 1 + x = -10.173494975 Solving 1 + x = -10.173494975 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 = -10.173494975 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.173494975 + -1 x = -10.173494975 + -1 Combine like terms: -10.173494975 + -1 = -11.173494975 x = -11.173494975 Simplifying x = -11.173494975Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.173494975, -11.173494975}
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