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Simplifying 3x2 + -430x + -11000 = 0 Reorder the terms: -11000 + -430x + 3x2 = 0 Solving -11000 + -430x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3666.666667 + -143.3333333x + x2 = 0 Move the constant term to the right: Add '3666.666667' to each side of the equation. -3666.666667 + -143.3333333x + 3666.666667 + x2 = 0 + 3666.666667 Reorder the terms: -3666.666667 + 3666.666667 + -143.3333333x + x2 = 0 + 3666.666667 Combine like terms: -3666.666667 + 3666.666667 = 0.000000 0.000000 + -143.3333333x + x2 = 0 + 3666.666667 -143.3333333x + x2 = 0 + 3666.666667 Combine like terms: 0 + 3666.666667 = 3666.666667 -143.3333333x + x2 = 3666.666667 The x term is -143.3333333x. Take half its coefficient (-71.66666665). Square it (5136.111109) and add it to both sides. Add '5136.111109' to each side of the equation. -143.3333333x + 5136.111109 + x2 = 3666.666667 + 5136.111109 Reorder the terms: 5136.111109 + -143.3333333x + x2 = 3666.666667 + 5136.111109 Combine like terms: 3666.666667 + 5136.111109 = 8802.777776 5136.111109 + -143.3333333x + x2 = 8802.777776 Factor a perfect square on the left side: (x + -71.66666665)(x + -71.66666665) = 8802.777776 Calculate the square root of the right side: 93.823119624 Break this problem into two subproblems by setting (x + -71.66666665) equal to 93.823119624 and -93.823119624.Subproblem 1
x + -71.66666665 = 93.823119624 Simplifying x + -71.66666665 = 93.823119624 Reorder the terms: -71.66666665 + x = 93.823119624 Solving -71.66666665 + x = 93.823119624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.66666665' to each side of the equation. -71.66666665 + 71.66666665 + x = 93.823119624 + 71.66666665 Combine like terms: -71.66666665 + 71.66666665 = 0.00000000 0.00000000 + x = 93.823119624 + 71.66666665 x = 93.823119624 + 71.66666665 Combine like terms: 93.823119624 + 71.66666665 = 165.489786274 x = 165.489786274 Simplifying x = 165.489786274Subproblem 2
x + -71.66666665 = -93.823119624 Simplifying x + -71.66666665 = -93.823119624 Reorder the terms: -71.66666665 + x = -93.823119624 Solving -71.66666665 + x = -93.823119624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '71.66666665' to each side of the equation. -71.66666665 + 71.66666665 + x = -93.823119624 + 71.66666665 Combine like terms: -71.66666665 + 71.66666665 = 0.00000000 0.00000000 + x = -93.823119624 + 71.66666665 x = -93.823119624 + 71.66666665 Combine like terms: -93.823119624 + 71.66666665 = -22.156452974 x = -22.156452974 Simplifying x = -22.156452974Solution
The solution to the problem is based on the solutions from the subproblems. x = {165.489786274, -22.156452974}
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