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Simplifying x2 + 4x = 22 Reorder the terms: 4x + x2 = 22 Solving 4x + x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + 4x + x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 4x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 4x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 4x + x2 = 0 + 22 4x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 4x + x2 = 22 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 = 22 + 4 Reorder the terms: 4 + 4x + x2 = 22 + 4 Combine like terms: 22 + 4 = 26 4 + 4x + x2 = 26 Factor a perfect square on the left side: (x + 2)(x + 2) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + 2) equal to 5.099019514 and -5.099019514.Subproblem 1
x + 2 = 5.099019514 Simplifying x + 2 = 5.099019514 Reorder the terms: 2 + x = 5.099019514 Solving 2 + x = 5.099019514 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 = 5.099019514 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.099019514 + -2 x = 5.099019514 + -2 Combine like terms: 5.099019514 + -2 = 3.099019514 x = 3.099019514 Simplifying x = 3.099019514Subproblem 2
x + 2 = -5.099019514 Simplifying x + 2 = -5.099019514 Reorder the terms: 2 + x = -5.099019514 Solving 2 + x = -5.099019514 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 = -5.099019514 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.099019514 + -2 x = -5.099019514 + -2 Combine like terms: -5.099019514 + -2 = -7.099019514 x = -7.099019514 Simplifying x = -7.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.099019514, -7.099019514}
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