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Simplifying 33 = 7x + x2 Solving 33 = 7x + x2 Solving for variable 'x'. Reorder the terms: 33 + -7x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 33 + -7x + -1x2 = 0 + x2 + -1x2 33 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 33 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -33 + 7x + x2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + 7x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 7x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 7x + x2 = 0 + 33 7x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 7x + x2 = 33 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 33 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 33 + 12.25 Combine like terms: 33 + 12.25 = 45.25 12.25 + 7x + x2 = 45.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + 3.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + 3.5 = 6.726812024 Simplifying x + 3.5 = 6.726812024 Reorder the terms: 3.5 + x = 6.726812024 Solving 3.5 + x = 6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.726812024 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.726812024 + -3.5 x = 6.726812024 + -3.5 Combine like terms: 6.726812024 + -3.5 = 3.226812024 x = 3.226812024 Simplifying x = 3.226812024Subproblem 2
x + 3.5 = -6.726812024 Simplifying x + 3.5 = -6.726812024 Reorder the terms: 3.5 + x = -6.726812024 Solving 3.5 + x = -6.726812024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.726812024 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.726812024 + -3.5 x = -6.726812024 + -3.5 Combine like terms: -6.726812024 + -3.5 = -10.226812024 x = -10.226812024 Simplifying x = -10.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.226812024, -10.226812024}
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