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Simplifying -2x2 + 5x + 13 = 0 Reorder the terms: 13 + 5x + -2x2 = 0 Solving 13 + 5x + -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 + -2.5x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -2.5x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -2.5x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -2.5x + x2 = 0 + 6.5 -2.5x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -2.5x + x2 = 6.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 6.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 6.5 + 1.5625 Combine like terms: 6.5 + 1.5625 = 8.0625 1.5625 + -2.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + -1.25) equal to 2.839454173 and -2.839454173.Subproblem 1
x + -1.25 = 2.839454173 Simplifying x + -1.25 = 2.839454173 Reorder the terms: -1.25 + x = 2.839454173 Solving -1.25 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.839454173 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.839454173 + 1.25 x = 2.839454173 + 1.25 Combine like terms: 2.839454173 + 1.25 = 4.089454173 x = 4.089454173 Simplifying x = 4.089454173Subproblem 2
x + -1.25 = -2.839454173 Simplifying x + -1.25 = -2.839454173 Reorder the terms: -1.25 + x = -2.839454173 Solving -1.25 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.839454173 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.839454173 + 1.25 x = -2.839454173 + 1.25 Combine like terms: -2.839454173 + 1.25 = -1.589454173 x = -1.589454173 Simplifying x = -1.589454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.089454173, -1.589454173}
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