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Simplifying 7(X2 + 2) + -1X = -8X + 55 Reorder the terms: 7(2 + X2) + -1X = -8X + 55 (2 * 7 + X2 * 7) + -1X = -8X + 55 (14 + 7X2) + -1X = -8X + 55 Reorder the terms: 14 + -1X + 7X2 = -8X + 55 Reorder the terms: 14 + -1X + 7X2 = 55 + -8X Solving 14 + -1X + 7X2 = 55 + -8X Solving for variable 'X'. Reorder the terms: 14 + -55 + -1X + 8X + 7X2 = 55 + -8X + -55 + 8X Combine like terms: 14 + -55 = -41 -41 + -1X + 8X + 7X2 = 55 + -8X + -55 + 8X Combine like terms: -1X + 8X = 7X -41 + 7X + 7X2 = 55 + -8X + -55 + 8X Reorder the terms: -41 + 7X + 7X2 = 55 + -55 + -8X + 8X Combine like terms: 55 + -55 = 0 -41 + 7X + 7X2 = 0 + -8X + 8X -41 + 7X + 7X2 = -8X + 8X Combine like terms: -8X + 8X = 0 -41 + 7X + 7X2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.857142857 + X + X2 = 0 Move the constant term to the right: Add '5.857142857' to each side of the equation. -5.857142857 + X + 5.857142857 + X2 = 0 + 5.857142857 Reorder the terms: -5.857142857 + 5.857142857 + X + X2 = 0 + 5.857142857 Combine like terms: -5.857142857 + 5.857142857 = 0.000000000 0.000000000 + X + X2 = 0 + 5.857142857 X + X2 = 0 + 5.857142857 Combine like terms: 0 + 5.857142857 = 5.857142857 X + X2 = 5.857142857 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. + 0.25 + X2 = 5.857142857 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + X2 = 5.857142857 + 0.25 Combine like terms: 5.857142857 + 0.25 = 6.107142857 1.25 + X2 = 6.107142857 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 6.107142857 Calculate the square root of the right side: 2.471263413 Break this problem into two subproblems by setting (X + 0.5) equal to 2.471263413 and -2.471263413.Subproblem 1
X + 0.5 = 2.471263413 Simplifying X + 0.5 = 2.471263413 Reorder the terms: 0.5 + X = 2.471263413 Solving 0.5 + X = 2.471263413 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 = 2.471263413 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 2.471263413 + -0.5 X = 2.471263413 + -0.5 Combine like terms: 2.471263413 + -0.5 = 1.971263413 X = 1.971263413 Simplifying X = 1.971263413Subproblem 2
X + 0.5 = -2.471263413 Simplifying X + 0.5 = -2.471263413 Reorder the terms: 0.5 + X = -2.471263413 Solving 0.5 + X = -2.471263413 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 = -2.471263413 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -2.471263413 + -0.5 X = -2.471263413 + -0.5 Combine like terms: -2.471263413 + -0.5 = -2.971263413 X = -2.971263413 Simplifying X = -2.971263413Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.971263413, -2.971263413}
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