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Simplifying 0.004X2 + X = 45.28 Reorder the terms: X + 0.004X2 = 45.28 Solving X + 0.004X2 = 45.28 Solving for variable 'X'. Reorder the terms: -45.28 + X + 0.004X2 = 45.28 + -45.28 Combine like terms: 45.28 + -45.28 = 0.00 -45.28 + X + 0.004X2 = 0.00 Begin completing the square. Divide all terms by 0.004 the coefficient of the squared term: Divide each side by '0.004'. -11320 + 250X + X2 = 0 Move the constant term to the right: Add '11320' to each side of the equation. -11320 + 250X + 11320 + X2 = 0 + 11320 Reorder the terms: -11320 + 11320 + 250X + X2 = 0 + 11320 Combine like terms: -11320 + 11320 = 0 0 + 250X + X2 = 0 + 11320 250X + X2 = 0 + 11320 Combine like terms: 0 + 11320 = 11320 250X + X2 = 11320 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. 250X + 0.25 + X2 = 11320 + 0.25 Reorder the terms: 0.25 + 250X + X2 = 11320 + 0.25 Combine like terms: 11320 + 0.25 = 11320.25 0.25 + 250X + X2 = 11320.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 11320.25 Calculate the square root of the right side: 106.396663482 Break this problem into two subproblems by setting (X + 0.5) equal to 106.396663482 and -106.396663482.Subproblem 1
X + 0.5 = 106.396663482 Simplifying X + 0.5 = 106.396663482 Reorder the terms: 0.5 + X = 106.396663482 Solving 0.5 + X = 106.396663482 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 = 106.396663482 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 106.396663482 + -0.5 X = 106.396663482 + -0.5 Combine like terms: 106.396663482 + -0.5 = 105.896663482 X = 105.896663482 Simplifying X = 105.896663482Subproblem 2
X + 0.5 = -106.396663482 Simplifying X + 0.5 = -106.396663482 Reorder the terms: 0.5 + X = -106.396663482 Solving 0.5 + X = -106.396663482 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 = -106.396663482 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -106.396663482 + -0.5 X = -106.396663482 + -0.5 Combine like terms: -106.396663482 + -0.5 = -106.896663482 X = -106.896663482 Simplifying X = -106.896663482Solution
The solution to the problem is based on the solutions from the subproblems. X = {105.896663482, -106.896663482}
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