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Simplifying x2 + 7x + -53 = 0 Reorder the terms: -53 + 7x + x2 = 0 Solving -53 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + 7x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + 7x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 7x + x2 = 0 + 53 7x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 7x + x2 = 53 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 = 53 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 53 + 12.25 Combine like terms: 53 + 12.25 = 65.25 12.25 + 7x + x2 = 65.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + 3.5) equal to 8.077747211 and -8.077747211.Subproblem 1
x + 3.5 = 8.077747211 Simplifying x + 3.5 = 8.077747211 Reorder the terms: 3.5 + x = 8.077747211 Solving 3.5 + x = 8.077747211 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 = 8.077747211 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 8.077747211 + -3.5 x = 8.077747211 + -3.5 Combine like terms: 8.077747211 + -3.5 = 4.577747211 x = 4.577747211 Simplifying x = 4.577747211Subproblem 2
x + 3.5 = -8.077747211 Simplifying x + 3.5 = -8.077747211 Reorder the terms: 3.5 + x = -8.077747211 Solving 3.5 + x = -8.077747211 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 = -8.077747211 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -8.077747211 + -3.5 x = -8.077747211 + -3.5 Combine like terms: -8.077747211 + -3.5 = -11.577747211 x = -11.577747211 Simplifying x = -11.577747211Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.577747211, -11.577747211}
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