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Simplifying -1x2 + 1x + 39 = 0 Reorder the terms: 39 + 1x + -1x2 = 0 Solving 39 + 1x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -39 + -1x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + -1x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -1x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -1x + x2 = 0 + 39 -1x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -1x + x2 = 39 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 39 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 39 + 0.25 Combine like terms: 39 + 0.25 = 39.25 0.25 + -1x + x2 = 39.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + -0.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + -0.5 = 6.264982043 Simplifying x + -0.5 = 6.264982043 Reorder the terms: -0.5 + x = 6.264982043 Solving -0.5 + x = 6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 6.264982043 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.264982043 + 0.5 x = 6.264982043 + 0.5 Combine like terms: 6.264982043 + 0.5 = 6.764982043 x = 6.764982043 Simplifying x = 6.764982043Subproblem 2
x + -0.5 = -6.264982043 Simplifying x + -0.5 = -6.264982043 Reorder the terms: -0.5 + x = -6.264982043 Solving -0.5 + x = -6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -6.264982043 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.264982043 + 0.5 x = -6.264982043 + 0.5 Combine like terms: -6.264982043 + 0.5 = -5.764982043 x = -5.764982043 Simplifying x = -5.764982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.764982043, -5.764982043}
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