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Simplifying x2 + 7x + -27 = 5 Reorder the terms: -27 + 7x + x2 = 5 Solving -27 + 7x + x2 = 5 Solving for variable 'x'. Reorder the terms: -27 + -5 + 7x + x2 = 5 + -5 Combine like terms: -27 + -5 = -32 -32 + 7x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -32 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 7x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 7x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 7x + x2 = 0 + 32 7x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 7x + x2 = 32 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 = 32 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 32 + 12.25 Combine like terms: 32 + 12.25 = 44.25 12.25 + 7x + x2 = 44.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + 3.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + 3.5 = 6.652067348 Simplifying x + 3.5 = 6.652067348 Reorder the terms: 3.5 + x = 6.652067348 Solving 3.5 + x = 6.652067348 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 = 6.652067348 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.652067348 + -3.5 x = 6.652067348 + -3.5 Combine like terms: 6.652067348 + -3.5 = 3.152067348 x = 3.152067348 Simplifying x = 3.152067348Subproblem 2
x + 3.5 = -6.652067348 Simplifying x + 3.5 = -6.652067348 Reorder the terms: 3.5 + x = -6.652067348 Solving 3.5 + x = -6.652067348 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 = -6.652067348 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.652067348 + -3.5 x = -6.652067348 + -3.5 Combine like terms: -6.652067348 + -3.5 = -10.152067348 x = -10.152067348 Simplifying x = -10.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.152067348, -10.152067348}
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