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Simplifying -16x2 + 96x + 265 = 0 Reorder the terms: 265 + 96x + -16x2 = 0 Solving 265 + 96x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -16.5625 + -6x + x2 = 0 Move the constant term to the right: Add '16.5625' to each side of the equation. -16.5625 + -6x + 16.5625 + x2 = 0 + 16.5625 Reorder the terms: -16.5625 + 16.5625 + -6x + x2 = 0 + 16.5625 Combine like terms: -16.5625 + 16.5625 = 0.0000 0.0000 + -6x + x2 = 0 + 16.5625 -6x + x2 = 0 + 16.5625 Combine like terms: 0 + 16.5625 = 16.5625 -6x + x2 = 16.5625 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 16.5625 + 9 Reorder the terms: 9 + -6x + x2 = 16.5625 + 9 Combine like terms: 16.5625 + 9 = 25.5625 9 + -6x + x2 = 25.5625 Factor a perfect square on the left side: (x + -3)(x + -3) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + -3) equal to 5.055937104 and -5.055937104.Subproblem 1
x + -3 = 5.055937104 Simplifying x + -3 = 5.055937104 Reorder the terms: -3 + x = 5.055937104 Solving -3 + x = 5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.055937104 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.055937104 + 3 x = 5.055937104 + 3 Combine like terms: 5.055937104 + 3 = 8.055937104 x = 8.055937104 Simplifying x = 8.055937104Subproblem 2
x + -3 = -5.055937104 Simplifying x + -3 = -5.055937104 Reorder the terms: -3 + x = -5.055937104 Solving -3 + x = -5.055937104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.055937104 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.055937104 + 3 x = -5.055937104 + 3 Combine like terms: -5.055937104 + 3 = -2.055937104 x = -2.055937104 Simplifying x = -2.055937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.055937104, -2.055937104}
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