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Simplifying x2 + -1x + -35.74 = 0 Reorder the terms: -35.74 + -1x + x2 = 0 Solving -35.74 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '35.74' to each side of the equation. -35.74 + -1x + 35.74 + x2 = 0 + 35.74 Reorder the terms: -35.74 + 35.74 + -1x + x2 = 0 + 35.74 Combine like terms: -35.74 + 35.74 = 0.00 0.00 + -1x + x2 = 0 + 35.74 -1x + x2 = 0 + 35.74 Combine like terms: 0 + 35.74 = 35.74 -1x + x2 = 35.74 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 = 35.74 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 35.74 + 0.25 Combine like terms: 35.74 + 0.25 = 35.99 0.25 + -1x + x2 = 35.99 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 35.99 Calculate the square root of the right side: 5.999166609 Break this problem into two subproblems by setting (x + -0.5) equal to 5.999166609 and -5.999166609.Subproblem 1
x + -0.5 = 5.999166609 Simplifying x + -0.5 = 5.999166609 Reorder the terms: -0.5 + x = 5.999166609 Solving -0.5 + x = 5.999166609 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 = 5.999166609 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.999166609 + 0.5 x = 5.999166609 + 0.5 Combine like terms: 5.999166609 + 0.5 = 6.499166609 x = 6.499166609 Simplifying x = 6.499166609Subproblem 2
x + -0.5 = -5.999166609 Simplifying x + -0.5 = -5.999166609 Reorder the terms: -0.5 + x = -5.999166609 Solving -0.5 + x = -5.999166609 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 = -5.999166609 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.999166609 + 0.5 x = -5.999166609 + 0.5 Combine like terms: -5.999166609 + 0.5 = -5.499166609 x = -5.499166609 Simplifying x = -5.499166609Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.499166609, -5.499166609}
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