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Simplifying 16x2 + 8x + 1 = 96 Reorder the terms: 1 + 8x + 16x2 = 96 Solving 1 + 8x + 16x2 = 96 Solving for variable 'x'. Reorder the terms: 1 + -96 + 8x + 16x2 = 96 + -96 Combine like terms: 1 + -96 = -95 -95 + 8x + 16x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -95 + 8x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.9375 + 0.5x + x2 = 0 Move the constant term to the right: Add '5.9375' to each side of the equation. -5.9375 + 0.5x + 5.9375 + x2 = 0 + 5.9375 Reorder the terms: -5.9375 + 5.9375 + 0.5x + x2 = 0 + 5.9375 Combine like terms: -5.9375 + 5.9375 = 0.0000 0.0000 + 0.5x + x2 = 0 + 5.9375 0.5x + x2 = 0 + 5.9375 Combine like terms: 0 + 5.9375 = 5.9375 0.5x + x2 = 5.9375 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 5.9375 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 5.9375 + 0.0625 Combine like terms: 5.9375 + 0.0625 = 6 0.0625 + 0.5x + x2 = 6 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 0.25) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 0.25 = 2.449489743 Simplifying x + 0.25 = 2.449489743 Reorder the terms: 0.25 + x = 2.449489743 Solving 0.25 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.449489743 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.449489743 + -0.25 x = 2.449489743 + -0.25 Combine like terms: 2.449489743 + -0.25 = 2.199489743 x = 2.199489743 Simplifying x = 2.199489743Subproblem 2
x + 0.25 = -2.449489743 Simplifying x + 0.25 = -2.449489743 Reorder the terms: 0.25 + x = -2.449489743 Solving 0.25 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.449489743 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.449489743 + -0.25 x = -2.449489743 + -0.25 Combine like terms: -2.449489743 + -0.25 = -2.699489743 x = -2.699489743 Simplifying x = -2.699489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.199489743, -2.699489743}
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