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Simplifying 8x2 + 29x + -11 = 0 Reorder the terms: -11 + 29x + 8x2 = 0 Solving -11 + 29x + 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'. -1.375 + 3.625x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 3.625x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 3.625x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 3.625x + x2 = 0 + 1.375 3.625x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 3.625x + x2 = 1.375 The x term is 3.625x. Take half its coefficient (1.8125). Square it (3.28515625) and add it to both sides. Add '3.28515625' to each side of the equation. 3.625x + 3.28515625 + x2 = 1.375 + 3.28515625 Reorder the terms: 3.28515625 + 3.625x + x2 = 1.375 + 3.28515625 Combine like terms: 1.375 + 3.28515625 = 4.66015625 3.28515625 + 3.625x + x2 = 4.66015625 Factor a perfect square on the left side: (x + 1.8125)(x + 1.8125) = 4.66015625 Calculate the square root of the right side: 2.158739505 Break this problem into two subproblems by setting (x + 1.8125) equal to 2.158739505 and -2.158739505.Subproblem 1
x + 1.8125 = 2.158739505 Simplifying x + 1.8125 = 2.158739505 Reorder the terms: 1.8125 + x = 2.158739505 Solving 1.8125 + x = 2.158739505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8125' to each side of the equation. 1.8125 + -1.8125 + x = 2.158739505 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + x = 2.158739505 + -1.8125 x = 2.158739505 + -1.8125 Combine like terms: 2.158739505 + -1.8125 = 0.346239505 x = 0.346239505 Simplifying x = 0.346239505Subproblem 2
x + 1.8125 = -2.158739505 Simplifying x + 1.8125 = -2.158739505 Reorder the terms: 1.8125 + x = -2.158739505 Solving 1.8125 + x = -2.158739505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8125' to each side of the equation. 1.8125 + -1.8125 + x = -2.158739505 + -1.8125 Combine like terms: 1.8125 + -1.8125 = 0.0000 0.0000 + x = -2.158739505 + -1.8125 x = -2.158739505 + -1.8125 Combine like terms: -2.158739505 + -1.8125 = -3.971239505 x = -3.971239505 Simplifying x = -3.971239505Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.346239505, -3.971239505}
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