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Simplifying 2x2 + 3x + -55 = 0 Reorder the terms: -55 + 3x + 2x2 = 0 Solving -55 + 3x + 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'. -27.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + 1.5x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + 1.5x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + 1.5x + x2 = 0 + 27.5 1.5x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 1.5x + x2 = 27.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 27.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 27.5 + 0.5625 Combine like terms: 27.5 + 0.5625 = 28.0625 0.5625 + 1.5x + x2 = 28.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 28.0625 Calculate the square root of the right side: 5.297405025 Break this problem into two subproblems by setting (x + 0.75) equal to 5.297405025 and -5.297405025.Subproblem 1
x + 0.75 = 5.297405025 Simplifying x + 0.75 = 5.297405025 Reorder the terms: 0.75 + x = 5.297405025 Solving 0.75 + x = 5.297405025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 5.297405025 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 5.297405025 + -0.75 x = 5.297405025 + -0.75 Combine like terms: 5.297405025 + -0.75 = 4.547405025 x = 4.547405025 Simplifying x = 4.547405025Subproblem 2
x + 0.75 = -5.297405025 Simplifying x + 0.75 = -5.297405025 Reorder the terms: 0.75 + x = -5.297405025 Solving 0.75 + x = -5.297405025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -5.297405025 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -5.297405025 + -0.75 x = -5.297405025 + -0.75 Combine like terms: -5.297405025 + -0.75 = -6.047405025 x = -6.047405025 Simplifying x = -6.047405025Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.547405025, -6.047405025}
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