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Simplifying 4.9X2 + 21X + -300 = 0 Reorder the terms: -300 + 21X + 4.9X2 = 0 Solving -300 + 21X + 4.9X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -61.2244898 + 4.285714286X + X2 = 0 Move the constant term to the right: Add '61.2244898' to each side of the equation. -61.2244898 + 4.285714286X + 61.2244898 + X2 = 0 + 61.2244898 Reorder the terms: -61.2244898 + 61.2244898 + 4.285714286X + X2 = 0 + 61.2244898 Combine like terms: -61.2244898 + 61.2244898 = 0.0000000 0.0000000 + 4.285714286X + X2 = 0 + 61.2244898 4.285714286X + X2 = 0 + 61.2244898 Combine like terms: 0 + 61.2244898 = 61.2244898 4.285714286X + X2 = 61.2244898 The X term is 4.285714286X. Take half its coefficient (2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. 4.285714286X + 4.591836735 + X2 = 61.2244898 + 4.591836735 Reorder the terms: 4.591836735 + 4.285714286X + X2 = 61.2244898 + 4.591836735 Combine like terms: 61.2244898 + 4.591836735 = 65.816326535 4.591836735 + 4.285714286X + X2 = 65.816326535 Factor a perfect square on the left side: (X + 2.142857143)(X + 2.142857143) = 65.816326535 Calculate the square root of the right side: 8.112726209 Break this problem into two subproblems by setting (X + 2.142857143) equal to 8.112726209 and -8.112726209.Subproblem 1
X + 2.142857143 = 8.112726209 Simplifying X + 2.142857143 = 8.112726209 Reorder the terms: 2.142857143 + X = 8.112726209 Solving 2.142857143 + X = 8.112726209 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + X = 8.112726209 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + X = 8.112726209 + -2.142857143 X = 8.112726209 + -2.142857143 Combine like terms: 8.112726209 + -2.142857143 = 5.969869066 X = 5.969869066 Simplifying X = 5.969869066Subproblem 2
X + 2.142857143 = -8.112726209 Simplifying X + 2.142857143 = -8.112726209 Reorder the terms: 2.142857143 + X = -8.112726209 Solving 2.142857143 + X = -8.112726209 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + X = -8.112726209 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + X = -8.112726209 + -2.142857143 X = -8.112726209 + -2.142857143 Combine like terms: -8.112726209 + -2.142857143 = -10.255583352 X = -10.255583352 Simplifying X = -10.255583352Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.969869066, -10.255583352}
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