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Simplifying (2x)(2x) + -1x + -1 = 0 Remove parenthesis around (2x) 2x(2x) + -1x + -1 = 0 Remove parenthesis around (2x) 2x * 2x + -1x + -1 = 0 Reorder the terms for easier multiplication: 2 * 2x * x + -1x + -1 = 0 Multiply 2 * 2 4x * x + -1x + -1 = 0 Multiply x * x 4x2 + -1x + -1 = 0 Reorder the terms: -1 + -1x + 4x2 = 0 Solving -1 + -1x + 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'. -0.25 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.25x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.25x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.25x + x2 = 0 + 0.25 -0.25x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.25x + x2 = 0.25 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.25 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.25 + 0.015625 Combine like terms: 0.25 + 0.015625 = 0.265625 0.015625 + -0.25x + x2 = 0.265625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (x + -0.125) equal to 0.515388203 and -0.515388203.Subproblem 1
x + -0.125 = 0.515388203 Simplifying x + -0.125 = 0.515388203 Reorder the terms: -0.125 + x = 0.515388203 Solving -0.125 + x = 0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.515388203 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.515388203 + 0.125 x = 0.515388203 + 0.125 Combine like terms: 0.515388203 + 0.125 = 0.640388203 x = 0.640388203 Simplifying x = 0.640388203Subproblem 2
x + -0.125 = -0.515388203 Simplifying x + -0.125 = -0.515388203 Reorder the terms: -0.125 + x = -0.515388203 Solving -0.125 + x = -0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.515388203 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.515388203 + 0.125 x = -0.515388203 + 0.125 Combine like terms: -0.515388203 + 0.125 = -0.390388203 x = -0.390388203 Simplifying x = -0.390388203Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.640388203, -0.390388203}
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