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Simplifying x + (x + -2)(x + 5) = 33 Reorder the terms: x + (-2 + x)(x + 5) = 33 Reorder the terms: x + (-2 + x)(5 + x) = 33 Multiply (-2 + x) * (5 + x) x + (-2(5 + x) + x(5 + x)) = 33 x + ((5 * -2 + x * -2) + x(5 + x)) = 33 x + ((-10 + -2x) + x(5 + x)) = 33 x + (-10 + -2x + (5 * x + x * x)) = 33 x + (-10 + -2x + (5x + x2)) = 33 Combine like terms: -2x + 5x = 3x x + (-10 + 3x + x2) = 33 Reorder the terms: -10 + x + 3x + x2 = 33 Combine like terms: x + 3x = 4x -10 + 4x + x2 = 33 Solving -10 + 4x + x2 = 33 Solving for variable 'x'. Reorder the terms: -10 + -33 + 4x + x2 = 33 + -33 Combine like terms: -10 + -33 = -43 -43 + 4x + x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -43 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 4x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + 4x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 4x + x2 = 0 + 43 4x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 4x + x2 = 43 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 43 + 4 Reorder the terms: 4 + 4x + x2 = 43 + 4 Combine like terms: 43 + 4 = 47 4 + 4x + x2 = 47 Factor a perfect square on the left side: (x + 2)(x + 2) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + 2) equal to 6.8556546 and -6.8556546.Subproblem 1
x + 2 = 6.8556546 Simplifying x + 2 = 6.8556546 Reorder the terms: 2 + x = 6.8556546 Solving 2 + x = 6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.8556546 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.8556546 + -2 x = 6.8556546 + -2 Combine like terms: 6.8556546 + -2 = 4.8556546 x = 4.8556546 Simplifying x = 4.8556546Subproblem 2
x + 2 = -6.8556546 Simplifying x + 2 = -6.8556546 Reorder the terms: 2 + x = -6.8556546 Solving 2 + x = -6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.8556546 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.8556546 + -2 x = -6.8556546 + -2 Combine like terms: -6.8556546 + -2 = -8.8556546 x = -8.8556546 Simplifying x = -8.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.8556546, -8.8556546}
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