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Simplifying 2x2 + -5x + -16 = 0 Reorder the terms: -16 + -5x + 2x2 = 0 Solving -16 + -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'. -8 + -2.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -2.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -2.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -2.5x + x2 = 0 + 8 -2.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -2.5x + x2 = 8 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 = 8 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 8 + 1.5625 Combine like terms: 8 + 1.5625 = 9.5625 1.5625 + -2.5x + x2 = 9.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (x + -1.25) equal to 3.092329219 and -3.092329219.Subproblem 1
x + -1.25 = 3.092329219 Simplifying x + -1.25 = 3.092329219 Reorder the terms: -1.25 + x = 3.092329219 Solving -1.25 + x = 3.092329219 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 = 3.092329219 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.092329219 + 1.25 x = 3.092329219 + 1.25 Combine like terms: 3.092329219 + 1.25 = 4.342329219 x = 4.342329219 Simplifying x = 4.342329219Subproblem 2
x + -1.25 = -3.092329219 Simplifying x + -1.25 = -3.092329219 Reorder the terms: -1.25 + x = -3.092329219 Solving -1.25 + x = -3.092329219 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 = -3.092329219 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.092329219 + 1.25 x = -3.092329219 + 1.25 Combine like terms: -3.092329219 + 1.25 = -1.842329219 x = -1.842329219 Simplifying x = -1.842329219Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.342329219, -1.842329219}
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