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Simplifying x + (x + 1) + x2 = 63 Reorder the terms: x + (1 + x) + x2 = 63 Remove parenthesis around (1 + x) x + 1 + x + x2 = 63 Reorder the terms: 1 + x + x + x2 = 63 Combine like terms: x + x = 2x 1 + 2x + x2 = 63 Solving 1 + 2x + x2 = 63 Solving for variable 'x'. Reorder the terms: 1 + -63 + 2x + x2 = 63 + -63 Combine like terms: 1 + -63 = -62 -62 + 2x + x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -62 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + 2x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + 2x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + 2x + x2 = 0 + 62 2x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 2x + x2 = 62 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 = 62 + 1 Reorder the terms: 1 + 2x + x2 = 62 + 1 Combine like terms: 62 + 1 = 63 1 + 2x + x2 = 63 Factor a perfect square on the left side: (x + 1)(x + 1) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + 1) equal to 7.937253933 and -7.937253933.Subproblem 1
x + 1 = 7.937253933 Simplifying x + 1 = 7.937253933 Reorder the terms: 1 + x = 7.937253933 Solving 1 + x = 7.937253933 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 = 7.937253933 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.937253933 + -1 x = 7.937253933 + -1 Combine like terms: 7.937253933 + -1 = 6.937253933 x = 6.937253933 Simplifying x = 6.937253933Subproblem 2
x + 1 = -7.937253933 Simplifying x + 1 = -7.937253933 Reorder the terms: 1 + x = -7.937253933 Solving 1 + x = -7.937253933 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 = -7.937253933 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.937253933 + -1 x = -7.937253933 + -1 Combine like terms: -7.937253933 + -1 = -8.937253933 x = -8.937253933 Simplifying x = -8.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.937253933, -8.937253933}
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