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Simplifying x(4 + x) = 33 (4 * x + x * x) = 33 (4x + x2) = 33 Solving 4x + x2 = 33 Solving for variable 'x'. Reorder the terms: -33 + 4x + x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 4x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 4x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 4x + x2 = 0 + 33 4x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 4x + x2 = 33 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 = 33 + 4 Reorder the terms: 4 + 4x + x2 = 33 + 4 Combine like terms: 33 + 4 = 37 4 + 4x + x2 = 37 Factor a perfect square on the left side: (x + 2)(x + 2) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + 2) equal to 6.08276253 and -6.08276253.Subproblem 1
x + 2 = 6.08276253 Simplifying x + 2 = 6.08276253 Reorder the terms: 2 + x = 6.08276253 Solving 2 + x = 6.08276253 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 = 6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.08276253 + -2 x = 6.08276253 + -2 Combine like terms: 6.08276253 + -2 = 4.08276253 x = 4.08276253 Simplifying x = 4.08276253Subproblem 2
x + 2 = -6.08276253 Simplifying x + 2 = -6.08276253 Reorder the terms: 2 + x = -6.08276253 Solving 2 + x = -6.08276253 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 = -6.08276253 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.08276253 + -2 x = -6.08276253 + -2 Combine like terms: -6.08276253 + -2 = -8.08276253 x = -8.08276253 Simplifying x = -8.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.08276253, -8.08276253}
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