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Simplifying 5x2 + 33x + -55 = 0 Reorder the terms: -55 + 33x + 5x2 = 0 Solving -55 + 33x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -11 + 6.6x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 6.6x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 6.6x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 6.6x + x2 = 0 + 11 6.6x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 6.6x + x2 = 11 The x term is 6.6x. Take half its coefficient (3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. 6.6x + 10.89 + x2 = 11 + 10.89 Reorder the terms: 10.89 + 6.6x + x2 = 11 + 10.89 Combine like terms: 11 + 10.89 = 21.89 10.89 + 6.6x + x2 = 21.89 Factor a perfect square on the left side: (x + 3.3)(x + 3.3) = 21.89 Calculate the square root of the right side: 4.678675026 Break this problem into two subproblems by setting (x + 3.3) equal to 4.678675026 and -4.678675026.Subproblem 1
x + 3.3 = 4.678675026 Simplifying x + 3.3 = 4.678675026 Reorder the terms: 3.3 + x = 4.678675026 Solving 3.3 + x = 4.678675026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + x = 4.678675026 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = 4.678675026 + -3.3 x = 4.678675026 + -3.3 Combine like terms: 4.678675026 + -3.3 = 1.378675026 x = 1.378675026 Simplifying x = 1.378675026Subproblem 2
x + 3.3 = -4.678675026 Simplifying x + 3.3 = -4.678675026 Reorder the terms: 3.3 + x = -4.678675026 Solving 3.3 + x = -4.678675026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + x = -4.678675026 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = -4.678675026 + -3.3 x = -4.678675026 + -3.3 Combine like terms: -4.678675026 + -3.3 = -7.978675026 x = -7.978675026 Simplifying x = -7.978675026Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.378675026, -7.978675026}
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