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Simplifying x2 + 4x = 29 Reorder the terms: 4x + x2 = 29 Solving 4x + x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + 4x + x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 4x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 4x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 4x + x2 = 0 + 29 4x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 4x + x2 = 29 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 = 29 + 4 Reorder the terms: 4 + 4x + x2 = 29 + 4 Combine like terms: 29 + 4 = 33 4 + 4x + x2 = 33 Factor a perfect square on the left side: (x + 2)(x + 2) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 2) equal to 5.744562647 and -5.744562647.Subproblem 1
x + 2 = 5.744562647 Simplifying x + 2 = 5.744562647 Reorder the terms: 2 + x = 5.744562647 Solving 2 + x = 5.744562647 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 = 5.744562647 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.744562647 + -2 x = 5.744562647 + -2 Combine like terms: 5.744562647 + -2 = 3.744562647 x = 3.744562647 Simplifying x = 3.744562647Subproblem 2
x + 2 = -5.744562647 Simplifying x + 2 = -5.744562647 Reorder the terms: 2 + x = -5.744562647 Solving 2 + x = -5.744562647 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 = -5.744562647 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.744562647 + -2 x = -5.744562647 + -2 Combine like terms: -5.744562647 + -2 = -7.744562647 x = -7.744562647 Simplifying x = -7.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.744562647, -7.744562647}
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