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Simplifying 8x2 + 16x + -66 = 3 Reorder the terms: -66 + 16x + 8x2 = 3 Solving -66 + 16x + 8x2 = 3 Solving for variable 'x'. Reorder the terms: -66 + -3 + 16x + 8x2 = 3 + -3 Combine like terms: -66 + -3 = -69 -69 + 16x + 8x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -69 + 16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -8.625 + 2x + x2 = 0 Move the constant term to the right: Add '8.625' to each side of the equation. -8.625 + 2x + 8.625 + x2 = 0 + 8.625 Reorder the terms: -8.625 + 8.625 + 2x + x2 = 0 + 8.625 Combine like terms: -8.625 + 8.625 = 0.000 0.000 + 2x + x2 = 0 + 8.625 2x + x2 = 0 + 8.625 Combine like terms: 0 + 8.625 = 8.625 2x + x2 = 8.625 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 = 8.625 + 1 Reorder the terms: 1 + 2x + x2 = 8.625 + 1 Combine like terms: 8.625 + 1 = 9.625 1 + 2x + x2 = 9.625 Factor a perfect square on the left side: (x + 1)(x + 1) = 9.625 Calculate the square root of the right side: 3.102418411 Break this problem into two subproblems by setting (x + 1) equal to 3.102418411 and -3.102418411.Subproblem 1
x + 1 = 3.102418411 Simplifying x + 1 = 3.102418411 Reorder the terms: 1 + x = 3.102418411 Solving 1 + x = 3.102418411 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 = 3.102418411 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.102418411 + -1 x = 3.102418411 + -1 Combine like terms: 3.102418411 + -1 = 2.102418411 x = 2.102418411 Simplifying x = 2.102418411Subproblem 2
x + 1 = -3.102418411 Simplifying x + 1 = -3.102418411 Reorder the terms: 1 + x = -3.102418411 Solving 1 + x = -3.102418411 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 = -3.102418411 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.102418411 + -1 x = -3.102418411 + -1 Combine like terms: -3.102418411 + -1 = -4.102418411 x = -4.102418411 Simplifying x = -4.102418411Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.102418411, -4.102418411}
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