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Simplifying x2 + 5 + -33 = 4x + 9 Reorder the terms: 5 + -33 + x2 = 4x + 9 Combine like terms: 5 + -33 = -28 -28 + x2 = 4x + 9 Reorder the terms: -28 + x2 = 9 + 4x Solving -28 + x2 = 9 + 4x Solving for variable 'x'. Reorder the terms: -28 + -9 + -4x + x2 = 9 + 4x + -9 + -4x Combine like terms: -28 + -9 = -37 -37 + -4x + x2 = 9 + 4x + -9 + -4x Reorder the terms: -37 + -4x + x2 = 9 + -9 + 4x + -4x Combine like terms: 9 + -9 = 0 -37 + -4x + x2 = 0 + 4x + -4x -37 + -4x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -37 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -4x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + -4x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -4x + x2 = 0 + 37 -4x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 -4x + x2 = 37 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 = 37 + 4 Reorder the terms: 4 + -4x + x2 = 37 + 4 Combine like terms: 37 + 4 = 41 4 + -4x + x2 = 41 Factor a perfect square on the left side: (x + -2)(x + -2) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + -2) equal to 6.403124237 and -6.403124237.Subproblem 1
x + -2 = 6.403124237 Simplifying x + -2 = 6.403124237 Reorder the terms: -2 + x = 6.403124237 Solving -2 + x = 6.403124237 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 = 6.403124237 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.403124237 + 2 x = 6.403124237 + 2 Combine like terms: 6.403124237 + 2 = 8.403124237 x = 8.403124237 Simplifying x = 8.403124237Subproblem 2
x + -2 = -6.403124237 Simplifying x + -2 = -6.403124237 Reorder the terms: -2 + x = -6.403124237 Solving -2 + x = -6.403124237 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 = -6.403124237 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.403124237 + 2 x = -6.403124237 + 2 Combine like terms: -6.403124237 + 2 = -4.403124237 x = -4.403124237 Simplifying x = -4.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.403124237, -4.403124237}
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