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Simplifying 29 = 7 + x(x + 2) Reorder the terms: 29 = 7 + x(2 + x) 29 = 7 + (2 * x + x * x) 29 = 7 + (2x + x2) Solving 29 = 7 + 2x + x2 Solving for variable 'x'. Combine like terms: 29 + -7 = 22 22 + -2x + -1x2 = 7 + 2x + x2 + -7 + -2x + -1x2 Reorder the terms: 22 + -2x + -1x2 = 7 + -7 + 2x + -2x + x2 + -1x2 Combine like terms: 7 + -7 = 0 22 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 22 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 22 + -2x + -1x2 = 0 + x2 + -1x2 22 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 22 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -22 + 2x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + 2x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 2x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 2x + x2 = 0 + 22 2x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 2x + x2 = 22 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 = 22 + 1 Reorder the terms: 1 + 2x + x2 = 22 + 1 Combine like terms: 22 + 1 = 23 1 + 2x + x2 = 23 Factor a perfect square on the left side: (x + 1)(x + 1) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 1) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 1 = 4.795831523 Simplifying x + 1 = 4.795831523 Reorder the terms: 1 + x = 4.795831523 Solving 1 + x = 4.795831523 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 = 4.795831523 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.795831523 + -1 x = 4.795831523 + -1 Combine like terms: 4.795831523 + -1 = 3.795831523 x = 3.795831523 Simplifying x = 3.795831523Subproblem 2
x + 1 = -4.795831523 Simplifying x + 1 = -4.795831523 Reorder the terms: 1 + x = -4.795831523 Solving 1 + x = -4.795831523 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 = -4.795831523 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.795831523 + -1 x = -4.795831523 + -1 Combine like terms: -4.795831523 + -1 = -5.795831523 x = -5.795831523 Simplifying x = -5.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.795831523, -5.795831523}
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