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Simplifying 0 = -4x2 + x + 1 Reorder the terms: 0 = 1 + x + -4x2 Solving 0 = 1 + x + -4x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -1x + 4x2 = 1 + x + -4x2 + -1 + -1x + 4x2 Reorder the terms: -1 + -1x + 4x2 = 1 + -1 + x + -1x + -4x2 + 4x2 Combine like terms: 1 + -1 = 0 -1 + -1x + 4x2 = 0 + x + -1x + -4x2 + 4x2 -1 + -1x + 4x2 = x + -1x + -4x2 + 4x2 Combine like terms: x + -1x = 0 -1 + -1x + 4x2 = 0 + -4x2 + 4x2 -1 + -1x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -1 + -1x + 4x2 = 0 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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