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Simplifying (2x + -1) = 4x(x + -2) Reorder the terms: (-1 + 2x) = 4x(x + -2) Remove parenthesis around (-1 + 2x) -1 + 2x = 4x(x + -2) Reorder the terms: -1 + 2x = 4x(-2 + x) -1 + 2x = (-2 * 4x + x * 4x) -1 + 2x = (-8x + 4x2) Solving -1 + 2x = -8x + 4x2 Solving for variable 'x'. Combine like terms: 2x + 8x = 10x -1 + 10x + -4x2 = -8x + 4x2 + 8x + -4x2 Reorder the terms: -1 + 10x + -4x2 = -8x + 8x + 4x2 + -4x2 Combine like terms: -8x + 8x = 0 -1 + 10x + -4x2 = 0 + 4x2 + -4x2 -1 + 10x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -1 + 10x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.25 + -2.5x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -2.5x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -2.5x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -2.5x + x2 = 0 + -0.25 -2.5x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -2.5x + x2 = -0.25 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -0.25 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -0.25 + 1.5625 Combine like terms: -0.25 + 1.5625 = 1.3125 1.5625 + -2.5x + x2 = 1.3125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (x + -1.25) equal to 1.145643924 and -1.145643924.Subproblem 1
x + -1.25 = 1.145643924 Simplifying x + -1.25 = 1.145643924 Reorder the terms: -1.25 + x = 1.145643924 Solving -1.25 + x = 1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.145643924 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.145643924 + 1.25 x = 1.145643924 + 1.25 Combine like terms: 1.145643924 + 1.25 = 2.395643924 x = 2.395643924 Simplifying x = 2.395643924Subproblem 2
x + -1.25 = -1.145643924 Simplifying x + -1.25 = -1.145643924 Reorder the terms: -1.25 + x = -1.145643924 Solving -1.25 + x = -1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.145643924 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.145643924 + 1.25 x = -1.145643924 + 1.25 Combine like terms: -1.145643924 + 1.25 = 0.104356076 x = 0.104356076 Simplifying x = 0.104356076Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.395643924, 0.104356076}
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