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Simplifying 2x2 + -5x + -120 = 0 Reorder the terms: -120 + -5x + 2x2 = 0 Solving -120 + -5x + 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'. -60 + -2.5x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -2.5x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -2.5x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -2.5x + x2 = 0 + 60 -2.5x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -2.5x + x2 = 60 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 = 60 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 60 + 1.5625 Combine like terms: 60 + 1.5625 = 61.5625 1.5625 + -2.5x + x2 = 61.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 61.5625 Calculate the square root of the right side: 7.846177413 Break this problem into two subproblems by setting (x + -1.25) equal to 7.846177413 and -7.846177413.Subproblem 1
x + -1.25 = 7.846177413 Simplifying x + -1.25 = 7.846177413 Reorder the terms: -1.25 + x = 7.846177413 Solving -1.25 + x = 7.846177413 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 = 7.846177413 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 7.846177413 + 1.25 x = 7.846177413 + 1.25 Combine like terms: 7.846177413 + 1.25 = 9.096177413 x = 9.096177413 Simplifying x = 9.096177413Subproblem 2
x + -1.25 = -7.846177413 Simplifying x + -1.25 = -7.846177413 Reorder the terms: -1.25 + x = -7.846177413 Solving -1.25 + x = -7.846177413 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 = -7.846177413 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -7.846177413 + 1.25 x = -7.846177413 + 1.25 Combine like terms: -7.846177413 + 1.25 = -6.596177413 x = -6.596177413 Simplifying x = -6.596177413Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.096177413, -6.596177413}
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