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Simplifying x(x + 0.5) = 2 Reorder the terms: x(0.5 + x) = 2 (0.5 * x + x * x) = 2 (0.5x + x2) = 2 Solving 0.5x + x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 0.5x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 0.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.5x + x2 = 0 + 2 0.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.5x + x2 = 2 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 2 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 2 + 0.0625 Combine like terms: 2 + 0.0625 = 2.0625 0.0625 + 0.5x + x2 = 2.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (x + 0.25) equal to 1.436140662 and -1.436140662.Subproblem 1
x + 0.25 = 1.436140662 Simplifying x + 0.25 = 1.436140662 Reorder the terms: 0.25 + x = 1.436140662 Solving 0.25 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.436140662 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.436140662 + -0.25 x = 1.436140662 + -0.25 Combine like terms: 1.436140662 + -0.25 = 1.186140662 x = 1.186140662 Simplifying x = 1.186140662Subproblem 2
x + 0.25 = -1.436140662 Simplifying x + 0.25 = -1.436140662 Reorder the terms: 0.25 + x = -1.436140662 Solving 0.25 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.436140662 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.436140662 + -0.25 x = -1.436140662 + -0.25 Combine like terms: -1.436140662 + -0.25 = -1.686140662 x = -1.686140662 Simplifying x = -1.686140662Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.186140662, -1.686140662}
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