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Simplifying 1.8X2 + 4X = 20 Reorder the terms: 4X + 1.8X2 = 20 Solving 4X + 1.8X2 = 20 Solving for variable 'X'. Reorder the terms: -20 + 4X + 1.8X2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 4X + 1.8X2 = 0 Begin completing the square. Divide all terms by 1.8 the coefficient of the squared term: Divide each side by '1.8'. -11.11111111 + 2.222222222X + X2 = 0 Move the constant term to the right: Add '11.11111111' to each side of the equation. -11.11111111 + 2.222222222X + 11.11111111 + X2 = 0 + 11.11111111 Reorder the terms: -11.11111111 + 11.11111111 + 2.222222222X + X2 = 0 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + 2.222222222X + X2 = 0 + 11.11111111 2.222222222X + X2 = 0 + 11.11111111 Combine like terms: 0 + 11.11111111 = 11.11111111 2.222222222X + X2 = 11.11111111 The X term is 2.222222222X. Take half its coefficient (1.111111111). Square it (1.234567901) and add it to both sides. Add '1.234567901' to each side of the equation. 2.222222222X + 1.234567901 + X2 = 11.11111111 + 1.234567901 Reorder the terms: 1.234567901 + 2.222222222X + X2 = 11.11111111 + 1.234567901 Combine like terms: 11.11111111 + 1.234567901 = 12.345679011 1.234567901 + 2.222222222X + X2 = 12.345679011 Factor a perfect square on the left side: (X + 1.111111111)(X + 1.111111111) = 12.345679011 Calculate the square root of the right side: 3.513641844 Break this problem into two subproblems by setting (X + 1.111111111) equal to 3.513641844 and -3.513641844.Subproblem 1
X + 1.111111111 = 3.513641844 Simplifying X + 1.111111111 = 3.513641844 Reorder the terms: 1.111111111 + X = 3.513641844 Solving 1.111111111 + X = 3.513641844 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + X = 3.513641844 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + X = 3.513641844 + -1.111111111 X = 3.513641844 + -1.111111111 Combine like terms: 3.513641844 + -1.111111111 = 2.402530733 X = 2.402530733 Simplifying X = 2.402530733Subproblem 2
X + 1.111111111 = -3.513641844 Simplifying X + 1.111111111 = -3.513641844 Reorder the terms: 1.111111111 + X = -3.513641844 Solving 1.111111111 + X = -3.513641844 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + X = -3.513641844 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + X = -3.513641844 + -1.111111111 X = -3.513641844 + -1.111111111 Combine like terms: -3.513641844 + -1.111111111 = -4.624752955 X = -4.624752955 Simplifying X = -4.624752955Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.402530733, -4.624752955}
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