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Simplifying x * x + 4x + 1 = 32 Multiply x * x x2 + 4x + 1 = 32 Reorder the terms: 1 + 4x + x2 = 32 Solving 1 + 4x + x2 = 32 Solving for variable 'x'. Reorder the terms: 1 + -32 + 4x + x2 = 32 + -32 Combine like terms: 1 + -32 = -31 -31 + 4x + x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -31 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 4x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 4x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 4x + x2 = 0 + 31 4x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 4x + x2 = 31 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 = 31 + 4 Reorder the terms: 4 + 4x + x2 = 31 + 4 Combine like terms: 31 + 4 = 35 4 + 4x + x2 = 35 Factor a perfect square on the left side: (x + 2)(x + 2) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + 2) equal to 5.916079783 and -5.916079783.Subproblem 1
x + 2 = 5.916079783 Simplifying x + 2 = 5.916079783 Reorder the terms: 2 + x = 5.916079783 Solving 2 + x = 5.916079783 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 = 5.916079783 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.916079783 + -2 x = 5.916079783 + -2 Combine like terms: 5.916079783 + -2 = 3.916079783 x = 3.916079783 Simplifying x = 3.916079783Subproblem 2
x + 2 = -5.916079783 Simplifying x + 2 = -5.916079783 Reorder the terms: 2 + x = -5.916079783 Solving 2 + x = -5.916079783 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 = -5.916079783 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.916079783 + -2 x = -5.916079783 + -2 Combine like terms: -5.916079783 + -2 = -7.916079783 x = -7.916079783 Simplifying x = -7.916079783Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.916079783, -7.916079783}
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