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Simplifying -2x2 + -16x + 5 = 0 Reorder the terms: 5 + -16x + -2x2 = 0 Solving 5 + -16x + -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'. -2.5 + 8x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 8x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 8x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 8x + x2 = 0 + 2.5 8x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 8x + x2 = 2.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 2.5 + 16 Reorder the terms: 16 + 8x + x2 = 2.5 + 16 Combine like terms: 2.5 + 16 = 18.5 16 + 8x + x2 = 18.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (x + 4) equal to 4.301162634 and -4.301162634.Subproblem 1
x + 4 = 4.301162634 Simplifying x + 4 = 4.301162634 Reorder the terms: 4 + x = 4.301162634 Solving 4 + x = 4.301162634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.301162634 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.301162634 + -4 x = 4.301162634 + -4 Combine like terms: 4.301162634 + -4 = 0.301162634 x = 0.301162634 Simplifying x = 0.301162634Subproblem 2
x + 4 = -4.301162634 Simplifying x + 4 = -4.301162634 Reorder the terms: 4 + x = -4.301162634 Solving 4 + x = -4.301162634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.301162634 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.301162634 + -4 x = -4.301162634 + -4 Combine like terms: -4.301162634 + -4 = -8.301162634 x = -8.301162634 Simplifying x = -8.301162634Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.301162634, -8.301162634}
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