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Simplifying 0.013x2 + -1.18x = 28.24 Reorder the terms: -1.18x + 0.013x2 = 28.24 Solving -1.18x + 0.013x2 = 28.24 Solving for variable 'x'. Reorder the terms: -28.24 + -1.18x + 0.013x2 = 28.24 + -28.24 Combine like terms: 28.24 + -28.24 = 0.00 -28.24 + -1.18x + 0.013x2 = 0.00 Begin completing the square. Divide all terms by 0.013 the coefficient of the squared term: Divide each side by '0.013'. -2172.307692 + -90.76923077x + x2 = 0 Move the constant term to the right: Add '2172.307692' to each side of the equation. -2172.307692 + -90.76923077x + 2172.307692 + x2 = 0 + 2172.307692 Reorder the terms: -2172.307692 + 2172.307692 + -90.76923077x + x2 = 0 + 2172.307692 Combine like terms: -2172.307692 + 2172.307692 = 0.000000 0.000000 + -90.76923077x + x2 = 0 + 2172.307692 -90.76923077x + x2 = 0 + 2172.307692 Combine like terms: 0 + 2172.307692 = 2172.307692 -90.76923077x + x2 = 2172.307692 The x term is -90.76923077x. Take half its coefficient (-45.38461539). Square it (2059.763314) and add it to both sides. Add '2059.763314' to each side of the equation. -90.76923077x + 2059.763314 + x2 = 2172.307692 + 2059.763314 Reorder the terms: 2059.763314 + -90.76923077x + x2 = 2172.307692 + 2059.763314 Combine like terms: 2172.307692 + 2059.763314 = 4232.071006 2059.763314 + -90.76923077x + x2 = 4232.071006 Factor a perfect square on the left side: (x + -45.38461539)(x + -45.38461539) = 4232.071006 Calculate the square root of the right side: 65.054369615 Break this problem into two subproblems by setting (x + -45.38461539) equal to 65.054369615 and -65.054369615.Subproblem 1
x + -45.38461539 = 65.054369615 Simplifying x + -45.38461539 = 65.054369615 Reorder the terms: -45.38461539 + x = 65.054369615 Solving -45.38461539 + x = 65.054369615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.38461539' to each side of the equation. -45.38461539 + 45.38461539 + x = 65.054369615 + 45.38461539 Combine like terms: -45.38461539 + 45.38461539 = 0.00000000 0.00000000 + x = 65.054369615 + 45.38461539 x = 65.054369615 + 45.38461539 Combine like terms: 65.054369615 + 45.38461539 = 110.438985005 x = 110.438985005 Simplifying x = 110.438985005Subproblem 2
x + -45.38461539 = -65.054369615 Simplifying x + -45.38461539 = -65.054369615 Reorder the terms: -45.38461539 + x = -65.054369615 Solving -45.38461539 + x = -65.054369615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.38461539' to each side of the equation. -45.38461539 + 45.38461539 + x = -65.054369615 + 45.38461539 Combine like terms: -45.38461539 + 45.38461539 = 0.00000000 0.00000000 + x = -65.054369615 + 45.38461539 x = -65.054369615 + 45.38461539 Combine like terms: -65.054369615 + 45.38461539 = -19.669754225 x = -19.669754225 Simplifying x = -19.669754225Solution
The solution to the problem is based on the solutions from the subproblems. x = {110.438985005, -19.669754225}
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