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Simplifying 3x2 + 253x = 120000 + -19500 + -6000 Reorder the terms: 253x + 3x2 = 120000 + -19500 + -6000 Combine like terms: 120000 + -19500 = 100500 253x + 3x2 = 100500 + -6000 Combine like terms: 100500 + -6000 = 94500 253x + 3x2 = 94500 Solving 253x + 3x2 = 94500 Solving for variable 'x'. Reorder the terms: -94500 + 253x + 3x2 = 94500 + -94500 Combine like terms: 94500 + -94500 = 0 -94500 + 253x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -31500 + 84.33333333x + x2 = 0 Move the constant term to the right: Add '31500' to each side of the equation. -31500 + 84.33333333x + 31500 + x2 = 0 + 31500 Reorder the terms: -31500 + 31500 + 84.33333333x + x2 = 0 + 31500 Combine like terms: -31500 + 31500 = 0 0 + 84.33333333x + x2 = 0 + 31500 84.33333333x + x2 = 0 + 31500 Combine like terms: 0 + 31500 = 31500 84.33333333x + x2 = 31500 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 = 31500 + 1778.027778 Reorder the terms: 1778.027778 + 84.33333333x + x2 = 31500 + 1778.027778 Combine like terms: 31500 + 1778.027778 = 33278.027778 1778.027778 + 84.33333333x + x2 = 33278.027778 Factor a perfect square on the left side: (x + 42.16666667)(x + 42.16666667) = 33278.027778 Calculate the square root of the right side: 182.422662457 Break this problem into two subproblems by setting (x + 42.16666667) equal to 182.422662457 and -182.422662457.Subproblem 1
x + 42.16666667 = 182.422662457 Simplifying x + 42.16666667 = 182.422662457 Reorder the terms: 42.16666667 + x = 182.422662457 Solving 42.16666667 + x = 182.422662457 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 = 182.422662457 + -42.16666667 Combine like terms: 42.16666667 + -42.16666667 = 0.00000000 0.00000000 + x = 182.422662457 + -42.16666667 x = 182.422662457 + -42.16666667 Combine like terms: 182.422662457 + -42.16666667 = 140.255995787 x = 140.255995787 Simplifying x = 140.255995787Subproblem 2
x + 42.16666667 = -182.422662457 Simplifying x + 42.16666667 = -182.422662457 Reorder the terms: 42.16666667 + x = -182.422662457 Solving 42.16666667 + x = -182.422662457 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 = -182.422662457 + -42.16666667 Combine like terms: 42.16666667 + -42.16666667 = 0.00000000 0.00000000 + x = -182.422662457 + -42.16666667 x = -182.422662457 + -42.16666667 Combine like terms: -182.422662457 + -42.16666667 = -224.589329127 x = -224.589329127 Simplifying x = -224.589329127Solution
The solution to the problem is based on the solutions from the subproblems. x = {140.255995787, -224.589329127}
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