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Simplifying 0 = 2x2 + -5x + -55 Reorder the terms: 0 = -55 + -5x + 2x2 Solving 0 = -55 + -5x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 55 = 55 55 + 5x + -2x2 = -55 + -5x + 2x2 + 55 + 5x + -2x2 Reorder the terms: 55 + 5x + -2x2 = -55 + 55 + -5x + 5x + 2x2 + -2x2 Combine like terms: -55 + 55 = 0 55 + 5x + -2x2 = 0 + -5x + 5x + 2x2 + -2x2 55 + 5x + -2x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 55 + 5x + -2x2 = 0 + 2x2 + -2x2 55 + 5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 55 + 5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -27.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + -2.5x + 27.5 + x2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + -2.5x + x2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + -2.5x + x2 = 0 + 27.5 -2.5x + x2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 -2.5x + x2 = 27.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 27.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 27.5 + 1.5625 Combine like terms: 27.5 + 1.5625 = 29.0625 1.5625 + -2.5x + x2 = 29.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 29.0625 Calculate the square root of the right side: 5.390964663 Break this problem into two subproblems by setting (x + -1.25) equal to 5.390964663 and -5.390964663.Subproblem 1
x + -1.25 = 5.390964663 Simplifying x + -1.25 = 5.390964663 Reorder the terms: -1.25 + x = 5.390964663 Solving -1.25 + x = 5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 5.390964663 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 5.390964663 + 1.25 x = 5.390964663 + 1.25 Combine like terms: 5.390964663 + 1.25 = 6.640964663 x = 6.640964663 Simplifying x = 6.640964663Subproblem 2
x + -1.25 = -5.390964663 Simplifying x + -1.25 = -5.390964663 Reorder the terms: -1.25 + x = -5.390964663 Solving -1.25 + x = -5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -5.390964663 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -5.390964663 + 1.25 x = -5.390964663 + 1.25 Combine like terms: -5.390964663 + 1.25 = -4.140964663 x = -4.140964663 Simplifying x = -4.140964663Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.640964663, -4.140964663}
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