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Simplifying 3x2 + 253x = 180000 Reorder the terms: 253x + 3x2 = 180000 Solving 253x + 3x2 = 180000 Solving for variable 'x'. Reorder the terms: -180000 + 253x + 3x2 = 180000 + -180000 Combine like terms: 180000 + -180000 = 0 -180000 + 253x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -60000 + 84.33333333x + x2 = 0 Move the constant term to the right: Add '60000' to each side of the equation. -60000 + 84.33333333x + 60000 + x2 = 0 + 60000 Reorder the terms: -60000 + 60000 + 84.33333333x + x2 = 0 + 60000 Combine like terms: -60000 + 60000 = 0 0 + 84.33333333x + x2 = 0 + 60000 84.33333333x + x2 = 0 + 60000 Combine like terms: 0 + 60000 = 60000 84.33333333x + x2 = 60000 The x term is 84.33333333x. Take half its coefficient (42.16666667). Square it (1778.027778) and add it to both sides. Add '1778.027778' to each side of the equation. 84.33333333x + 1778.027778 + x2 = 60000 + 1778.027778 Reorder the terms: 1778.027778 + 84.33333333x + x2 = 60000 + 1778.027778 Combine like terms: 60000 + 1778.027778 = 61778.027778 1778.027778 + 84.33333333x + x2 = 61778.027778 Factor a perfect square on the left side: (x + 42.16666667)(x + 42.16666667) = 61778.027778 Calculate the square root of the right side: 248.551861345 Break this problem into two subproblems by setting (x + 42.16666667) equal to 248.551861345 and -248.551861345.Subproblem 1
x + 42.16666667 = 248.551861345 Simplifying x + 42.16666667 = 248.551861345 Reorder the terms: 42.16666667 + x = 248.551861345 Solving 42.16666667 + x = 248.551861345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.16666667' to each side of the equation. 42.16666667 + -42.16666667 + x = 248.551861345 + -42.16666667 Combine like terms: 42.16666667 + -42.16666667 = 0.00000000 0.00000000 + x = 248.551861345 + -42.16666667 x = 248.551861345 + -42.16666667 Combine like terms: 248.551861345 + -42.16666667 = 206.385194675 x = 206.385194675 Simplifying x = 206.385194675Subproblem 2
x + 42.16666667 = -248.551861345 Simplifying x + 42.16666667 = -248.551861345 Reorder the terms: 42.16666667 + x = -248.551861345 Solving 42.16666667 + x = -248.551861345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.16666667' to each side of the equation. 42.16666667 + -42.16666667 + x = -248.551861345 + -42.16666667 Combine like terms: 42.16666667 + -42.16666667 = 0.00000000 0.00000000 + x = -248.551861345 + -42.16666667 x = -248.551861345 + -42.16666667 Combine like terms: -248.551861345 + -42.16666667 = -290.718528015 x = -290.718528015 Simplifying x = -290.718528015Solution
The solution to the problem is based on the solutions from the subproblems. x = {206.385194675, -290.718528015}
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