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Simplifying 8(x2 + 2x + 1) = -3 + 8 Reorder the terms: 8(1 + 2x + x2) = -3 + 8 (1 * 8 + 2x * 8 + x2 * 8) = -3 + 8 (8 + 16x + 8x2) = -3 + 8 Combine like terms: -3 + 8 = 5 8 + 16x + 8x2 = 5 Solving 8 + 16x + 8x2 = 5 Solving for variable 'x'. Reorder the terms: 8 + -5 + 16x + 8x2 = 5 + -5 Combine like terms: 8 + -5 = 3 3 + 16x + 8x2 = 5 + -5 Combine like terms: 5 + -5 = 0 3 + 16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 2x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 2x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 2x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 2x + x2 = 0 + -0.375 2x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 2x + x2 = -0.375 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.375 + 1 Reorder the terms: 1 + 2x + x2 = -0.375 + 1 Combine like terms: -0.375 + 1 = 0.625 1 + 2x + x2 = 0.625 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.625 Calculate the square root of the right side: 0.790569415 Break this problem into two subproblems by setting (x + 1) equal to 0.790569415 and -0.790569415.Subproblem 1
x + 1 = 0.790569415 Simplifying x + 1 = 0.790569415 Reorder the terms: 1 + x = 0.790569415 Solving 1 + x = 0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.790569415 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.790569415 + -1 x = 0.790569415 + -1 Combine like terms: 0.790569415 + -1 = -0.209430585 x = -0.209430585 Simplifying x = -0.209430585Subproblem 2
x + 1 = -0.790569415 Simplifying x + 1 = -0.790569415 Reorder the terms: 1 + x = -0.790569415 Solving 1 + x = -0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.790569415 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.790569415 + -1 x = -0.790569415 + -1 Combine like terms: -0.790569415 + -1 = -1.790569415 x = -1.790569415 Simplifying x = -1.790569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.209430585, -1.790569415}
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