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Simplifying 900000 = 425x2 + 45500x Reorder the terms: 900000 = 45500x + 425x2 Solving 900000 = 45500x + 425x2 Solving for variable 'x'. Reorder the terms: 900000 + -45500x + -425x2 = 45500x + -45500x + 425x2 + -425x2 Combine like terms: 45500x + -45500x = 0 900000 + -45500x + -425x2 = 0 + 425x2 + -425x2 900000 + -45500x + -425x2 = 425x2 + -425x2 Combine like terms: 425x2 + -425x2 = 0 900000 + -45500x + -425x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(36000 + -1820x + -17x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(36000 + -1820x + -17x2)' equal to zero and attempt to solve: Simplifying 36000 + -1820x + -17x2 = 0 Solving 36000 + -1820x + -17x2 = 0 Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -2117.647059 + 107.0588235x + x2 = 0 Move the constant term to the right: Add '2117.647059' to each side of the equation. -2117.647059 + 107.0588235x + 2117.647059 + x2 = 0 + 2117.647059 Reorder the terms: -2117.647059 + 2117.647059 + 107.0588235x + x2 = 0 + 2117.647059 Combine like terms: -2117.647059 + 2117.647059 = 0.000000 0.000000 + 107.0588235x + x2 = 0 + 2117.647059 107.0588235x + x2 = 0 + 2117.647059 Combine like terms: 0 + 2117.647059 = 2117.647059 107.0588235x + x2 = 2117.647059 The x term is 107.0588235x. Take half its coefficient (53.52941175). Square it (2865.397922) and add it to both sides. Add '2865.397922' to each side of the equation. 107.0588235x + 2865.397922 + x2 = 2117.647059 + 2865.397922 Reorder the terms: 2865.397922 + 107.0588235x + x2 = 2117.647059 + 2865.397922 Combine like terms: 2117.647059 + 2865.397922 = 4983.044981 2865.397922 + 107.0588235x + x2 = 4983.044981 Factor a perfect square on the left side: (x + 53.52941175)(x + 53.52941175) = 4983.044981 Calculate the square root of the right side: 70.59068622 Break this problem into two subproblems by setting (x + 53.52941175) equal to 70.59068622 and -70.59068622.Subproblem 1
x + 53.52941175 = 70.59068622 Simplifying x + 53.52941175 = 70.59068622 Reorder the terms: 53.52941175 + x = 70.59068622 Solving 53.52941175 + x = 70.59068622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-53.52941175' to each side of the equation. 53.52941175 + -53.52941175 + x = 70.59068622 + -53.52941175 Combine like terms: 53.52941175 + -53.52941175 = 0.00000000 0.00000000 + x = 70.59068622 + -53.52941175 x = 70.59068622 + -53.52941175 Combine like terms: 70.59068622 + -53.52941175 = 17.06127447 x = 17.06127447 Simplifying x = 17.06127447Subproblem 2
x + 53.52941175 = -70.59068622 Simplifying x + 53.52941175 = -70.59068622 Reorder the terms: 53.52941175 + x = -70.59068622 Solving 53.52941175 + x = -70.59068622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-53.52941175' to each side of the equation. 53.52941175 + -53.52941175 + x = -70.59068622 + -53.52941175 Combine like terms: 53.52941175 + -53.52941175 = 0.00000000 0.00000000 + x = -70.59068622 + -53.52941175 x = -70.59068622 + -53.52941175 Combine like terms: -70.59068622 + -53.52941175 = -124.12009797 x = -124.12009797 Simplifying x = -124.12009797Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.06127447, -124.12009797}Solution
x = {17.06127447, -124.12009797}
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