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Simplifying x2 + 7x + -86 = 0 Reorder the terms: -86 + 7x + x2 = 0 Solving -86 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '86' to each side of the equation. -86 + 7x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + 7x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + 7x + x2 = 0 + 86 7x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 7x + x2 = 86 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 = 86 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 86 + 12.25 Combine like terms: 86 + 12.25 = 98.25 12.25 + 7x + x2 = 98.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 98.25 Calculate the square root of the right side: 9.912113801 Break this problem into two subproblems by setting (x + 3.5) equal to 9.912113801 and -9.912113801.Subproblem 1
x + 3.5 = 9.912113801 Simplifying x + 3.5 = 9.912113801 Reorder the terms: 3.5 + x = 9.912113801 Solving 3.5 + x = 9.912113801 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 = 9.912113801 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.912113801 + -3.5 x = 9.912113801 + -3.5 Combine like terms: 9.912113801 + -3.5 = 6.412113801 x = 6.412113801 Simplifying x = 6.412113801Subproblem 2
x + 3.5 = -9.912113801 Simplifying x + 3.5 = -9.912113801 Reorder the terms: 3.5 + x = -9.912113801 Solving 3.5 + x = -9.912113801 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 = -9.912113801 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.912113801 + -3.5 x = -9.912113801 + -3.5 Combine like terms: -9.912113801 + -3.5 = -13.412113801 x = -13.412113801 Simplifying x = -13.412113801Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.412113801, -13.412113801}
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