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Simplifying -2x2 + 2x + 17 = 0 Reorder the terms: 17 + 2x + -2x2 = 0 Solving 17 + 2x + -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'. -8.5 + -1x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -1x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -1x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -1x + x2 = 0 + 8.5 -1x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -1x + x2 = 8.5 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 = 8.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 8.5 + 0.25 Combine like terms: 8.5 + 0.25 = 8.75 0.25 + -1x + x2 = 8.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + -0.5) equal to 2.958039892 and -2.958039892.Subproblem 1
x + -0.5 = 2.958039892 Simplifying x + -0.5 = 2.958039892 Reorder the terms: -0.5 + x = 2.958039892 Solving -0.5 + x = 2.958039892 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 = 2.958039892 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.958039892 + 0.5 x = 2.958039892 + 0.5 Combine like terms: 2.958039892 + 0.5 = 3.458039892 x = 3.458039892 Simplifying x = 3.458039892Subproblem 2
x + -0.5 = -2.958039892 Simplifying x + -0.5 = -2.958039892 Reorder the terms: -0.5 + x = -2.958039892 Solving -0.5 + x = -2.958039892 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 = -2.958039892 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.958039892 + 0.5 x = -2.958039892 + 0.5 Combine like terms: -2.958039892 + 0.5 = -2.458039892 x = -2.458039892 Simplifying x = -2.458039892Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.458039892, -2.458039892}
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