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Simplifying x2 + 7x + -324 = 0 Reorder the terms: -324 + 7x + x2 = 0 Solving -324 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '324' to each side of the equation. -324 + 7x + 324 + x2 = 0 + 324 Reorder the terms: -324 + 324 + 7x + x2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 7x + x2 = 0 + 324 7x + x2 = 0 + 324 Combine like terms: 0 + 324 = 324 7x + x2 = 324 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 = 324 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 324 + 12.25 Combine like terms: 324 + 12.25 = 336.25 12.25 + 7x + x2 = 336.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 336.25 Calculate the square root of the right side: 18.337120821 Break this problem into two subproblems by setting (x + 3.5) equal to 18.337120821 and -18.337120821.Subproblem 1
x + 3.5 = 18.337120821 Simplifying x + 3.5 = 18.337120821 Reorder the terms: 3.5 + x = 18.337120821 Solving 3.5 + x = 18.337120821 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 = 18.337120821 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 18.337120821 + -3.5 x = 18.337120821 + -3.5 Combine like terms: 18.337120821 + -3.5 = 14.837120821 x = 14.837120821 Simplifying x = 14.837120821Subproblem 2
x + 3.5 = -18.337120821 Simplifying x + 3.5 = -18.337120821 Reorder the terms: 3.5 + x = -18.337120821 Solving 3.5 + x = -18.337120821 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 = -18.337120821 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -18.337120821 + -3.5 x = -18.337120821 + -3.5 Combine like terms: -18.337120821 + -3.5 = -21.837120821 x = -21.837120821 Simplifying x = -21.837120821Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.837120821, -21.837120821}
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