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Simplifying x2 + 6x + -2674 = 0 Reorder the terms: -2674 + 6x + x2 = 0 Solving -2674 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2674' to each side of the equation. -2674 + 6x + 2674 + x2 = 0 + 2674 Reorder the terms: -2674 + 2674 + 6x + x2 = 0 + 2674 Combine like terms: -2674 + 2674 = 0 0 + 6x + x2 = 0 + 2674 6x + x2 = 0 + 2674 Combine like terms: 0 + 2674 = 2674 6x + x2 = 2674 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 2674 + 9 Reorder the terms: 9 + 6x + x2 = 2674 + 9 Combine like terms: 2674 + 9 = 2683 9 + 6x + x2 = 2683 Factor a perfect square on the left side: (x + 3)(x + 3) = 2683 Calculate the square root of the right side: 51.797683346 Break this problem into two subproblems by setting (x + 3) equal to 51.797683346 and -51.797683346.Subproblem 1
x + 3 = 51.797683346 Simplifying x + 3 = 51.797683346 Reorder the terms: 3 + x = 51.797683346 Solving 3 + x = 51.797683346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 51.797683346 + -3 Combine like terms: 3 + -3 = 0 0 + x = 51.797683346 + -3 x = 51.797683346 + -3 Combine like terms: 51.797683346 + -3 = 48.797683346 x = 48.797683346 Simplifying x = 48.797683346Subproblem 2
x + 3 = -51.797683346 Simplifying x + 3 = -51.797683346 Reorder the terms: 3 + x = -51.797683346 Solving 3 + x = -51.797683346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -51.797683346 + -3 Combine like terms: 3 + -3 = 0 0 + x = -51.797683346 + -3 x = -51.797683346 + -3 Combine like terms: -51.797683346 + -3 = -54.797683346 x = -54.797683346 Simplifying x = -54.797683346Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.797683346, -54.797683346}
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