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Simplifying 2x2 + 55x + -3 = 0 Reorder the terms: -3 + 55x + 2x2 = 0 Solving -3 + 55x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 27.5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 27.5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 27.5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 27.5x + x2 = 0 + 1.5 27.5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 27.5x + x2 = 1.5 The x term is 27.5x. Take half its coefficient (13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. 27.5x + 189.0625 + x2 = 1.5 + 189.0625 Reorder the terms: 189.0625 + 27.5x + x2 = 1.5 + 189.0625 Combine like terms: 1.5 + 189.0625 = 190.5625 189.0625 + 27.5x + x2 = 190.5625 Factor a perfect square on the left side: (x + 13.75)(x + 13.75) = 190.5625 Calculate the square root of the right side: 13.804437692 Break this problem into two subproblems by setting (x + 13.75) equal to 13.804437692 and -13.804437692.Subproblem 1
x + 13.75 = 13.804437692 Simplifying x + 13.75 = 13.804437692 Reorder the terms: 13.75 + x = 13.804437692 Solving 13.75 + x = 13.804437692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = 13.804437692 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = 13.804437692 + -13.75 x = 13.804437692 + -13.75 Combine like terms: 13.804437692 + -13.75 = 0.054437692 x = 0.054437692 Simplifying x = 0.054437692Subproblem 2
x + 13.75 = -13.804437692 Simplifying x + 13.75 = -13.804437692 Reorder the terms: 13.75 + x = -13.804437692 Solving 13.75 + x = -13.804437692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = -13.804437692 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = -13.804437692 + -13.75 x = -13.804437692 + -13.75 Combine like terms: -13.804437692 + -13.75 = -27.554437692 x = -27.554437692 Simplifying x = -27.554437692Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.054437692, -27.554437692}
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