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Simplifying -2x2 + 6x + 13 = 0 Reorder the terms: 13 + 6x + -2x2 = 0 Solving 13 + 6x + -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'. -6.5 + -3x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -3x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -3x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -3x + x2 = 0 + 6.5 -3x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -3x + x2 = 6.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 6.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 6.5 + 2.25 Combine like terms: 6.5 + 2.25 = 8.75 2.25 + -3x + x2 = 8.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + -1.5) equal to 2.958039892 and -2.958039892.Subproblem 1
x + -1.5 = 2.958039892 Simplifying x + -1.5 = 2.958039892 Reorder the terms: -1.5 + x = 2.958039892 Solving -1.5 + x = 2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.958039892 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.958039892 + 1.5 x = 2.958039892 + 1.5 Combine like terms: 2.958039892 + 1.5 = 4.458039892 x = 4.458039892 Simplifying x = 4.458039892Subproblem 2
x + -1.5 = -2.958039892 Simplifying x + -1.5 = -2.958039892 Reorder the terms: -1.5 + x = -2.958039892 Solving -1.5 + x = -2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.958039892 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.958039892 + 1.5 x = -2.958039892 + 1.5 Combine like terms: -2.958039892 + 1.5 = -1.458039892 x = -1.458039892 Simplifying x = -1.458039892Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.458039892, -1.458039892}
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