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Simplifying 50 = 4.9X2 + 5X Reorder the terms: 50 = 5X + 4.9X2 Solving 50 = 5X + 4.9X2 Solving for variable 'X'. Reorder the terms: 50 + -5X + -4.9X2 = 5X + -5X + 4.9X2 + -4.9X2 Combine like terms: 5X + -5X = 0 50 + -5X + -4.9X2 = 0 + 4.9X2 + -4.9X2 50 + -5X + -4.9X2 = 4.9X2 + -4.9X2 Combine like terms: 4.9X2 + -4.9X2 = 0.0 50 + -5X + -4.9X2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -10.20408163 + 1.020408163X + X2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 1.020408163X + 10.20408163 + X2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 1.020408163X + X2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 1.020408163X + X2 = 0 + 10.20408163 1.020408163X + X2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 1.020408163X + X2 = 10.20408163 The X term is 1.020408163X. Take half its coefficient (0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. 1.020408163X + 0.2603082048 + X2 = 10.20408163 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163X + X2 = 10.20408163 + 0.2603082048 Combine like terms: 10.20408163 + 0.2603082048 = 10.4643898348 0.2603082048 + 1.020408163X + X2 = 10.4643898348 Factor a perfect square on the left side: (X + 0.5102040815)(X + 0.5102040815) = 10.4643898348 Calculate the square root of the right side: 3.234870915 Break this problem into two subproblems by setting (X + 0.5102040815) equal to 3.234870915 and -3.234870915.Subproblem 1
X + 0.5102040815 = 3.234870915 Simplifying X + 0.5102040815 = 3.234870915 Reorder the terms: 0.5102040815 + X = 3.234870915 Solving 0.5102040815 + X = 3.234870915 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + X = 3.234870915 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + X = 3.234870915 + -0.5102040815 X = 3.234870915 + -0.5102040815 Combine like terms: 3.234870915 + -0.5102040815 = 2.7246668335 X = 2.7246668335 Simplifying X = 2.7246668335Subproblem 2
X + 0.5102040815 = -3.234870915 Simplifying X + 0.5102040815 = -3.234870915 Reorder the terms: 0.5102040815 + X = -3.234870915 Solving 0.5102040815 + X = -3.234870915 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + X = -3.234870915 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + X = -3.234870915 + -0.5102040815 X = -3.234870915 + -0.5102040815 Combine like terms: -3.234870915 + -0.5102040815 = -3.7450749965 X = -3.7450749965 Simplifying X = -3.7450749965Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.7246668335, -3.7450749965}
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