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Simplifying x2 + 7x + -308 = 0 Reorder the terms: -308 + 7x + x2 = 0 Solving -308 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '308' to each side of the equation. -308 + 7x + 308 + x2 = 0 + 308 Reorder the terms: -308 + 308 + 7x + x2 = 0 + 308 Combine like terms: -308 + 308 = 0 0 + 7x + x2 = 0 + 308 7x + x2 = 0 + 308 Combine like terms: 0 + 308 = 308 7x + x2 = 308 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 = 308 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 308 + 12.25 Combine like terms: 308 + 12.25 = 320.25 12.25 + 7x + x2 = 320.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 320.25 Calculate the square root of the right side: 17.895530168 Break this problem into two subproblems by setting (x + 3.5) equal to 17.895530168 and -17.895530168.Subproblem 1
x + 3.5 = 17.895530168 Simplifying x + 3.5 = 17.895530168 Reorder the terms: 3.5 + x = 17.895530168 Solving 3.5 + x = 17.895530168 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 = 17.895530168 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 17.895530168 + -3.5 x = 17.895530168 + -3.5 Combine like terms: 17.895530168 + -3.5 = 14.395530168 x = 14.395530168 Simplifying x = 14.395530168Subproblem 2
x + 3.5 = -17.895530168 Simplifying x + 3.5 = -17.895530168 Reorder the terms: 3.5 + x = -17.895530168 Solving 3.5 + x = -17.895530168 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 = -17.895530168 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -17.895530168 + -3.5 x = -17.895530168 + -3.5 Combine like terms: -17.895530168 + -3.5 = -21.395530168 x = -21.395530168 Simplifying x = -21.395530168Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.395530168, -21.395530168}
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