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Simplifying x(x + 1) + x = 50 Reorder the terms: x(1 + x) + x = 50 (1 * x + x * x) + x = 50 (1x + x2) + x = 50 Reorder the terms: 1x + x + x2 = 50 Combine like terms: 1x + x = 2x 2x + x2 = 50 Solving 2x + x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 2x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 2x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 2x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 2x + x2 = 0 + 50 2x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 2x + x2 = 50 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 = 50 + 1 Reorder the terms: 1 + 2x + x2 = 50 + 1 Combine like terms: 50 + 1 = 51 1 + 2x + x2 = 51 Factor a perfect square on the left side: (x + 1)(x + 1) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + 1) equal to 7.141428429 and -7.141428429.Subproblem 1
x + 1 = 7.141428429 Simplifying x + 1 = 7.141428429 Reorder the terms: 1 + x = 7.141428429 Solving 1 + x = 7.141428429 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 = 7.141428429 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.141428429 + -1 x = 7.141428429 + -1 Combine like terms: 7.141428429 + -1 = 6.141428429 x = 6.141428429 Simplifying x = 6.141428429Subproblem 2
x + 1 = -7.141428429 Simplifying x + 1 = -7.141428429 Reorder the terms: 1 + x = -7.141428429 Solving 1 + x = -7.141428429 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 = -7.141428429 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.141428429 + -1 x = -7.141428429 + -1 Combine like terms: -7.141428429 + -1 = -8.141428429 x = -8.141428429 Simplifying x = -8.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.141428429, -8.141428429}
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