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Simplifying 2200x + -17x2 + -1x3 = 0 Solving 2200x + -17x2 + -1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2200 + -17x + -1x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(2200 + -17x + -1x2)' equal to zero and attempt to solve: Simplifying 2200 + -17x + -1x2 = 0 Solving 2200 + -17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2200 + 17x + x2 = 0 Move the constant term to the right: Add '2200' to each side of the equation. -2200 + 17x + 2200 + x2 = 0 + 2200 Reorder the terms: -2200 + 2200 + 17x + x2 = 0 + 2200 Combine like terms: -2200 + 2200 = 0 0 + 17x + x2 = 0 + 2200 17x + x2 = 0 + 2200 Combine like terms: 0 + 2200 = 2200 17x + x2 = 2200 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 2200 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 2200 + 72.25 Combine like terms: 2200 + 72.25 = 2272.25 72.25 + 17x + x2 = 2272.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 2272.25 Calculate the square root of the right side: 47.668123521 Break this problem into two subproblems by setting (x + 8.5) equal to 47.668123521 and -47.668123521.Subproblem 1
x + 8.5 = 47.668123521 Simplifying x + 8.5 = 47.668123521 Reorder the terms: 8.5 + x = 47.668123521 Solving 8.5 + x = 47.668123521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 47.668123521 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 47.668123521 + -8.5 x = 47.668123521 + -8.5 Combine like terms: 47.668123521 + -8.5 = 39.168123521 x = 39.168123521 Simplifying x = 39.168123521Subproblem 2
x + 8.5 = -47.668123521 Simplifying x + 8.5 = -47.668123521 Reorder the terms: 8.5 + x = -47.668123521 Solving 8.5 + x = -47.668123521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -47.668123521 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -47.668123521 + -8.5 x = -47.668123521 + -8.5 Combine like terms: -47.668123521 + -8.5 = -56.168123521 x = -56.168123521 Simplifying x = -56.168123521Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.168123521, -56.168123521}Solution
x = {0, 39.168123521, -56.168123521}
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