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Simplifying X = 1.02X * X + -100 Multiply X * X X = 1.02X2 + -100 Reorder the terms: X = -100 + 1.02X2 Solving X = -100 + 1.02X2 Solving for variable 'X'. Reorder the terms: 100 + X + -1.02X2 = -100 + 1.02X2 + 100 + -1.02X2 Reorder the terms: 100 + X + -1.02X2 = -100 + 100 + 1.02X2 + -1.02X2 Combine like terms: -100 + 100 = 0 100 + X + -1.02X2 = 0 + 1.02X2 + -1.02X2 100 + X + -1.02X2 = 1.02X2 + -1.02X2 Combine like terms: 1.02X2 + -1.02X2 = 0.00 100 + X + -1.02X2 = 0.00 Begin completing the square. Divide all terms by -1.02 the coefficient of the squared term: Divide each side by '-1.02'. -98.03921569 + -0.9803921569X + X2 = 0 Move the constant term to the right: Add '98.03921569' to each side of the equation. -98.03921569 + -0.9803921569X + 98.03921569 + X2 = 0 + 98.03921569 Reorder the terms: -98.03921569 + 98.03921569 + -0.9803921569X + X2 = 0 + 98.03921569 Combine like terms: -98.03921569 + 98.03921569 = 0.00000000 0.00000000 + -0.9803921569X + X2 = 0 + 98.03921569 -0.9803921569X + X2 = 0 + 98.03921569 Combine like terms: 0 + 98.03921569 = 98.03921569 -0.9803921569X + X2 = 98.03921569 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.9803921569X + 0.25 + X2 = 98.03921569 + 0.25 Reorder the terms: 0.25 + -0.9803921569X + X2 = 98.03921569 + 0.25 Combine like terms: 98.03921569 + 0.25 = 98.28921569 0.25 + -0.9803921569X + X2 = 98.28921569 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 98.28921569 Calculate the square root of the right side: 9.914091773 Break this problem into two subproblems by setting (X + 0.5) equal to 9.914091773 and -9.914091773.Subproblem 1
X + 0.5 = 9.914091773 Simplifying X + 0.5 = 9.914091773 Reorder the terms: 0.5 + X = 9.914091773 Solving 0.5 + X = 9.914091773 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 9.914091773 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 9.914091773 + -0.5 X = 9.914091773 + -0.5 Combine like terms: 9.914091773 + -0.5 = 9.414091773 X = 9.414091773 Simplifying X = 9.414091773Subproblem 2
X + 0.5 = -9.914091773 Simplifying X + 0.5 = -9.914091773 Reorder the terms: 0.5 + X = -9.914091773 Solving 0.5 + X = -9.914091773 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -9.914091773 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -9.914091773 + -0.5 X = -9.914091773 + -0.5 Combine like terms: -9.914091773 + -0.5 = -10.414091773 X = -10.414091773 Simplifying X = -10.414091773Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.414091773, -10.414091773}
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