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Simplifying -1x2 + 1x + 0.41 = 0 Reorder the terms: 0.41 + 1x + -1x2 = 0 Solving 0.41 + 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'. -0.41 + -1x + x2 = 0 Move the constant term to the right: Add '0.41' to each side of the equation. -0.41 + -1x + 0.41 + x2 = 0 + 0.41 Reorder the terms: -0.41 + 0.41 + -1x + x2 = 0 + 0.41 Combine like terms: -0.41 + 0.41 = 0.00 0.00 + -1x + x2 = 0 + 0.41 -1x + x2 = 0 + 0.41 Combine like terms: 0 + 0.41 = 0.41 -1x + x2 = 0.41 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 = 0.41 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.41 + 0.25 Combine like terms: 0.41 + 0.25 = 0.66 0.25 + -1x + x2 = 0.66 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.66 Calculate the square root of the right side: 0.81240384 Break this problem into two subproblems by setting (x + -0.5) equal to 0.81240384 and -0.81240384.Subproblem 1
x + -0.5 = 0.81240384 Simplifying x + -0.5 = 0.81240384 Reorder the terms: -0.5 + x = 0.81240384 Solving -0.5 + x = 0.81240384 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 = 0.81240384 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.81240384 + 0.5 x = 0.81240384 + 0.5 Combine like terms: 0.81240384 + 0.5 = 1.31240384 x = 1.31240384 Simplifying x = 1.31240384Subproblem 2
x + -0.5 = -0.81240384 Simplifying x + -0.5 = -0.81240384 Reorder the terms: -0.5 + x = -0.81240384 Solving -0.5 + x = -0.81240384 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 = -0.81240384 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.81240384 + 0.5 x = -0.81240384 + 0.5 Combine like terms: -0.81240384 + 0.5 = -0.31240384 x = -0.31240384 Simplifying x = -0.31240384Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.31240384, -0.31240384}
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