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Simplifying -0.01X2 + 0.04X = -98.6 Reorder the terms: 0.04X + -0.01X2 = -98.6 Solving 0.04X + -0.01X2 = -98.6 Solving for variable 'X'. Reorder the terms: 98.6 + 0.04X + -0.01X2 = -98.6 + 98.6 Combine like terms: -98.6 + 98.6 = 0.0 98.6 + 0.04X + -0.01X2 = 0.0 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -9860 + -4X + X2 = 0 Move the constant term to the right: Add '9860' to each side of the equation. -9860 + -4X + 9860 + X2 = 0 + 9860 Reorder the terms: -9860 + 9860 + -4X + X2 = 0 + 9860 Combine like terms: -9860 + 9860 = 0 0 + -4X + X2 = 0 + 9860 -4X + X2 = 0 + 9860 Combine like terms: 0 + 9860 = 9860 -4X + X2 = 9860 The X term is -4X. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4X + 4 + X2 = 9860 + 4 Reorder the terms: 4 + -4X + X2 = 9860 + 4 Combine like terms: 9860 + 4 = 9864 4 + -4X + X2 = 9864 Factor a perfect square on the left side: (X + -2)(X + -2) = 9864 Calculate the square root of the right side: 99.317672143 Break this problem into two subproblems by setting (X + -2) equal to 99.317672143 and -99.317672143.Subproblem 1
X + -2 = 99.317672143 Simplifying X + -2 = 99.317672143 Reorder the terms: -2 + X = 99.317672143 Solving -2 + X = 99.317672143 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + X = 99.317672143 + 2 Combine like terms: -2 + 2 = 0 0 + X = 99.317672143 + 2 X = 99.317672143 + 2 Combine like terms: 99.317672143 + 2 = 101.317672143 X = 101.317672143 Simplifying X = 101.317672143Subproblem 2
X + -2 = -99.317672143 Simplifying X + -2 = -99.317672143 Reorder the terms: -2 + X = -99.317672143 Solving -2 + X = -99.317672143 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + X = -99.317672143 + 2 Combine like terms: -2 + 2 = 0 0 + X = -99.317672143 + 2 X = -99.317672143 + 2 Combine like terms: -99.317672143 + 2 = -97.317672143 X = -97.317672143 Simplifying X = -97.317672143Solution
The solution to the problem is based on the solutions from the subproblems. X = {101.317672143, -97.317672143}
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