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Simplifying 8x2 + 16x + -77 = 0 Reorder the terms: -77 + 16x + 8x2 = 0 Solving -77 + 16x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -9.625 + 2x + x2 = 0 Move the constant term to the right: Add '9.625' to each side of the equation. -9.625 + 2x + 9.625 + x2 = 0 + 9.625 Reorder the terms: -9.625 + 9.625 + 2x + x2 = 0 + 9.625 Combine like terms: -9.625 + 9.625 = 0.000 0.000 + 2x + x2 = 0 + 9.625 2x + x2 = 0 + 9.625 Combine like terms: 0 + 9.625 = 9.625 2x + x2 = 9.625 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 = 9.625 + 1 Reorder the terms: 1 + 2x + x2 = 9.625 + 1 Combine like terms: 9.625 + 1 = 10.625 1 + 2x + x2 = 10.625 Factor a perfect square on the left side: (x + 1)(x + 1) = 10.625 Calculate the square root of the right side: 3.259601203 Break this problem into two subproblems by setting (x + 1) equal to 3.259601203 and -3.259601203.Subproblem 1
x + 1 = 3.259601203 Simplifying x + 1 = 3.259601203 Reorder the terms: 1 + x = 3.259601203 Solving 1 + x = 3.259601203 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 = 3.259601203 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.259601203 + -1 x = 3.259601203 + -1 Combine like terms: 3.259601203 + -1 = 2.259601203 x = 2.259601203 Simplifying x = 2.259601203Subproblem 2
x + 1 = -3.259601203 Simplifying x + 1 = -3.259601203 Reorder the terms: 1 + x = -3.259601203 Solving 1 + x = -3.259601203 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 = -3.259601203 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.259601203 + -1 x = -3.259601203 + -1 Combine like terms: -3.259601203 + -1 = -4.259601203 x = -4.259601203 Simplifying x = -4.259601203Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.259601203, -4.259601203}
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