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Simplifying 2x(1 + -2x) + 5 = 0 (1 * 2x + -2x * 2x) + 5 = 0 (2x + -4x2) + 5 = 0 Reorder the terms: 5 + 2x + -4x2 = 0 Solving 5 + 2x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -0.5x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -0.5x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.5x + x2 = 0 + 1.25 -0.5x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -0.5x + x2 = 1.25 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 = 1.25 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.25 + 0.0625 Combine like terms: 1.25 + 0.0625 = 1.3125 0.0625 + -0.5x + x2 = 1.3125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (x + -0.25) equal to 1.145643924 and -1.145643924.Subproblem 1
x + -0.25 = 1.145643924 Simplifying x + -0.25 = 1.145643924 Reorder the terms: -0.25 + x = 1.145643924 Solving -0.25 + x = 1.145643924 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 = 1.145643924 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.145643924 + 0.25 x = 1.145643924 + 0.25 Combine like terms: 1.145643924 + 0.25 = 1.395643924 x = 1.395643924 Simplifying x = 1.395643924Subproblem 2
x + -0.25 = -1.145643924 Simplifying x + -0.25 = -1.145643924 Reorder the terms: -0.25 + x = -1.145643924 Solving -0.25 + x = -1.145643924 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 = -1.145643924 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.145643924 + 0.25 x = -1.145643924 + 0.25 Combine like terms: -1.145643924 + 0.25 = -0.895643924 x = -0.895643924 Simplifying x = -0.895643924Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.395643924, -0.895643924}
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