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Simplifying 2x2 + 5x = 120 Reorder the terms: 5x + 2x2 = 120 Solving 5x + 2x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 5x + 2x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 5x + 2x2 = 0 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 = 6.596177413 x = 6.596177413 Simplifying x = 6.596177413Subproblem 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 = -9.096177413 x = -9.096177413 Simplifying x = -9.096177413Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.596177413, -9.096177413}
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