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Simplifying 2x2 + 1x + -256 = 0 Reorder the terms: -256 + 1x + 2x2 = 0 Solving -256 + 1x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -128 + 0.5x + x2 = 0 Move the constant term to the right: Add '128' to each side of the equation. -128 + 0.5x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 0.5x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 0.5x + x2 = 0 + 128 0.5x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 0.5x + x2 = 128 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 = 128 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 128 + 0.0625 Combine like terms: 128 + 0.0625 = 128.0625 0.0625 + 0.5x + x2 = 128.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 128.0625 Calculate the square root of the right side: 11.316470298 Break this problem into two subproblems by setting (x + 0.25) equal to 11.316470298 and -11.316470298.Subproblem 1
x + 0.25 = 11.316470298 Simplifying x + 0.25 = 11.316470298 Reorder the terms: 0.25 + x = 11.316470298 Solving 0.25 + x = 11.316470298 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 = 11.316470298 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 11.316470298 + -0.25 x = 11.316470298 + -0.25 Combine like terms: 11.316470298 + -0.25 = 11.066470298 x = 11.066470298 Simplifying x = 11.066470298Subproblem 2
x + 0.25 = -11.316470298 Simplifying x + 0.25 = -11.316470298 Reorder the terms: 0.25 + x = -11.316470298 Solving 0.25 + x = -11.316470298 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 = -11.316470298 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -11.316470298 + -0.25 x = -11.316470298 + -0.25 Combine like terms: -11.316470298 + -0.25 = -11.566470298 x = -11.566470298 Simplifying x = -11.566470298Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.066470298, -11.566470298}
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