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Simplifying 126 = x2 + 2x Reorder the terms: 126 = 2x + x2 Solving 126 = 2x + x2 Solving for variable 'x'. Reorder the terms: 126 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 126 + -2x + -1x2 = 0 + x2 + -1x2 126 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 126 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -126 + 2x + x2 = 0 Move the constant term to the right: Add '126' to each side of the equation. -126 + 2x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + 2x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + 2x + x2 = 0 + 126 2x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 2x + x2 = 126 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 = 126 + 1 Reorder the terms: 1 + 2x + x2 = 126 + 1 Combine like terms: 126 + 1 = 127 1 + 2x + x2 = 127 Factor a perfect square on the left side: (x + 1)(x + 1) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (x + 1) equal to 11.26942767 and -11.26942767.Subproblem 1
x + 1 = 11.26942767 Simplifying x + 1 = 11.26942767 Reorder the terms: 1 + x = 11.26942767 Solving 1 + x = 11.26942767 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 = 11.26942767 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.26942767 + -1 x = 11.26942767 + -1 Combine like terms: 11.26942767 + -1 = 10.26942767 x = 10.26942767 Simplifying x = 10.26942767Subproblem 2
x + 1 = -11.26942767 Simplifying x + 1 = -11.26942767 Reorder the terms: 1 + x = -11.26942767 Solving 1 + x = -11.26942767 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 = -11.26942767 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.26942767 + -1 x = -11.26942767 + -1 Combine like terms: -11.26942767 + -1 = -12.26942767 x = -12.26942767 Simplifying x = -12.26942767Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.26942767, -12.26942767}
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