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Simplifying 0.289X2 + 0.1207X = 0.71 Reorder the terms: 0.1207X + 0.289X2 = 0.71 Solving 0.1207X + 0.289X2 = 0.71 Solving for variable 'X'. Reorder the terms: -0.71 + 0.1207X + 0.289X2 = 0.71 + -0.71 Combine like terms: 0.71 + -0.71 = 0.00 -0.71 + 0.1207X + 0.289X2 = 0.00 Begin completing the square. Divide all terms by 0.289 the coefficient of the squared term: Divide each side by '0.289'. -2.456747405 + 0.4176470588X + X2 = 0 Move the constant term to the right: Add '2.456747405' to each side of the equation. -2.456747405 + 0.4176470588X + 2.456747405 + X2 = 0 + 2.456747405 Reorder the terms: -2.456747405 + 2.456747405 + 0.4176470588X + X2 = 0 + 2.456747405 Combine like terms: -2.456747405 + 2.456747405 = 0.000000000 0.000000000 + 0.4176470588X + X2 = 0 + 2.456747405 0.4176470588X + X2 = 0 + 2.456747405 Combine like terms: 0 + 2.456747405 = 2.456747405 0.4176470588X + X2 = 2.456747405 The X term is 0.4176470588X. Take half its coefficient (0.2088235294). Square it (0.04360726643) and add it to both sides. Add '0.04360726643' to each side of the equation. 0.4176470588X + 0.04360726643 + X2 = 2.456747405 + 0.04360726643 Reorder the terms: 0.04360726643 + 0.4176470588X + X2 = 2.456747405 + 0.04360726643 Combine like terms: 2.456747405 + 0.04360726643 = 2.50035467143 0.04360726643 + 0.4176470588X + X2 = 2.50035467143 Factor a perfect square on the left side: (X + 0.2088235294)(X + 0.2088235294) = 2.50035467143 Calculate the square root of the right side: 1.581250983 Break this problem into two subproblems by setting (X + 0.2088235294) equal to 1.581250983 and -1.581250983.Subproblem 1
X + 0.2088235294 = 1.581250983 Simplifying X + 0.2088235294 = 1.581250983 Reorder the terms: 0.2088235294 + X = 1.581250983 Solving 0.2088235294 + X = 1.581250983 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.2088235294' to each side of the equation. 0.2088235294 + -0.2088235294 + X = 1.581250983 + -0.2088235294 Combine like terms: 0.2088235294 + -0.2088235294 = 0.0000000000 0.0000000000 + X = 1.581250983 + -0.2088235294 X = 1.581250983 + -0.2088235294 Combine like terms: 1.581250983 + -0.2088235294 = 1.3724274536 X = 1.3724274536 Simplifying X = 1.3724274536Subproblem 2
X + 0.2088235294 = -1.581250983 Simplifying X + 0.2088235294 = -1.581250983 Reorder the terms: 0.2088235294 + X = -1.581250983 Solving 0.2088235294 + X = -1.581250983 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.2088235294' to each side of the equation. 0.2088235294 + -0.2088235294 + X = -1.581250983 + -0.2088235294 Combine like terms: 0.2088235294 + -0.2088235294 = 0.0000000000 0.0000000000 + X = -1.581250983 + -0.2088235294 X = -1.581250983 + -0.2088235294 Combine like terms: -1.581250983 + -0.2088235294 = -1.7900745124 X = -1.7900745124 Simplifying X = -1.7900745124Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.3724274536, -1.7900745124}
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