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Simplifying 16x2 + 96x + 15 = 0 Reorder the terms: 15 + 96x + 16x2 = 0 Solving 15 + 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'. 0.9375 + 6x + x2 = 0 Move the constant term to the right: Add '-0.9375' to each side of the equation. 0.9375 + 6x + -0.9375 + x2 = 0 + -0.9375 Reorder the terms: 0.9375 + -0.9375 + 6x + x2 = 0 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + 6x + x2 = 0 + -0.9375 6x + x2 = 0 + -0.9375 Combine like terms: 0 + -0.9375 = -0.9375 6x + x2 = -0.9375 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 = -0.9375 + 9 Reorder the terms: 9 + 6x + x2 = -0.9375 + 9 Combine like terms: -0.9375 + 9 = 8.0625 9 + 6x + x2 = 8.0625 Factor a perfect square on the left side: (x + 3)(x + 3) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + 3) equal to 2.839454173 and -2.839454173.Subproblem 1
x + 3 = 2.839454173 Simplifying x + 3 = 2.839454173 Reorder the terms: 3 + x = 2.839454173 Solving 3 + x = 2.839454173 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 = 2.839454173 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.839454173 + -3 x = 2.839454173 + -3 Combine like terms: 2.839454173 + -3 = -0.160545827 x = -0.160545827 Simplifying x = -0.160545827Subproblem 2
x + 3 = -2.839454173 Simplifying x + 3 = -2.839454173 Reorder the terms: 3 + x = -2.839454173 Solving 3 + x = -2.839454173 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 = -2.839454173 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.839454173 + -3 x = -2.839454173 + -3 Combine like terms: -2.839454173 + -3 = -5.839454173 x = -5.839454173 Simplifying x = -5.839454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.160545827, -5.839454173}
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