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Simplifying 9x2 + 480x + -2000 = 0 Reorder the terms: -2000 + 480x + 9x2 = 0 Solving -2000 + 480x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -222.2222222 + 53.33333333x + x2 = 0 Move the constant term to the right: Add '222.2222222' to each side of the equation. -222.2222222 + 53.33333333x + 222.2222222 + x2 = 0 + 222.2222222 Reorder the terms: -222.2222222 + 222.2222222 + 53.33333333x + x2 = 0 + 222.2222222 Combine like terms: -222.2222222 + 222.2222222 = 0.0000000 0.0000000 + 53.33333333x + x2 = 0 + 222.2222222 53.33333333x + x2 = 0 + 222.2222222 Combine like terms: 0 + 222.2222222 = 222.2222222 53.33333333x + x2 = 222.2222222 The x term is 53.33333333x. Take half its coefficient (26.66666667). Square it (711.1111113) and add it to both sides. Add '711.1111113' to each side of the equation. 53.33333333x + 711.1111113 + x2 = 222.2222222 + 711.1111113 Reorder the terms: 711.1111113 + 53.33333333x + x2 = 222.2222222 + 711.1111113 Combine like terms: 222.2222222 + 711.1111113 = 933.3333335 711.1111113 + 53.33333333x + x2 = 933.3333335 Factor a perfect square on the left side: (x + 26.66666667)(x + 26.66666667) = 933.3333335 Calculate the square root of the right side: 30.550504636 Break this problem into two subproblems by setting (x + 26.66666667) equal to 30.550504636 and -30.550504636.Subproblem 1
x + 26.66666667 = 30.550504636 Simplifying x + 26.66666667 = 30.550504636 Reorder the terms: 26.66666667 + x = 30.550504636 Solving 26.66666667 + x = 30.550504636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.66666667' to each side of the equation. 26.66666667 + -26.66666667 + x = 30.550504636 + -26.66666667 Combine like terms: 26.66666667 + -26.66666667 = 0.00000000 0.00000000 + x = 30.550504636 + -26.66666667 x = 30.550504636 + -26.66666667 Combine like terms: 30.550504636 + -26.66666667 = 3.883837966 x = 3.883837966 Simplifying x = 3.883837966Subproblem 2
x + 26.66666667 = -30.550504636 Simplifying x + 26.66666667 = -30.550504636 Reorder the terms: 26.66666667 + x = -30.550504636 Solving 26.66666667 + x = -30.550504636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.66666667' to each side of the equation. 26.66666667 + -26.66666667 + x = -30.550504636 + -26.66666667 Combine like terms: 26.66666667 + -26.66666667 = 0.00000000 0.00000000 + x = -30.550504636 + -26.66666667 x = -30.550504636 + -26.66666667 Combine like terms: -30.550504636 + -26.66666667 = -57.217171306 x = -57.217171306 Simplifying x = -57.217171306Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.883837966, -57.217171306}
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