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Simplifying x2 + 6x + -15470 = 0 Reorder the terms: -15470 + 6x + x2 = 0 Solving -15470 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '15470' to each side of the equation. -15470 + 6x + 15470 + x2 = 0 + 15470 Reorder the terms: -15470 + 15470 + 6x + x2 = 0 + 15470 Combine like terms: -15470 + 15470 = 0 0 + 6x + x2 = 0 + 15470 6x + x2 = 0 + 15470 Combine like terms: 0 + 15470 = 15470 6x + x2 = 15470 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 = 15470 + 9 Reorder the terms: 9 + 6x + x2 = 15470 + 9 Combine like terms: 15470 + 9 = 15479 9 + 6x + x2 = 15479 Factor a perfect square on the left side: (x + 3)(x + 3) = 15479 Calculate the square root of the right side: 124.414629365 Break this problem into two subproblems by setting (x + 3) equal to 124.414629365 and -124.414629365.Subproblem 1
x + 3 = 124.414629365 Simplifying x + 3 = 124.414629365 Reorder the terms: 3 + x = 124.414629365 Solving 3 + x = 124.414629365 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 = 124.414629365 + -3 Combine like terms: 3 + -3 = 0 0 + x = 124.414629365 + -3 x = 124.414629365 + -3 Combine like terms: 124.414629365 + -3 = 121.414629365 x = 121.414629365 Simplifying x = 121.414629365Subproblem 2
x + 3 = -124.414629365 Simplifying x + 3 = -124.414629365 Reorder the terms: 3 + x = -124.414629365 Solving 3 + x = -124.414629365 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 = -124.414629365 + -3 Combine like terms: 3 + -3 = 0 0 + x = -124.414629365 + -3 x = -124.414629365 + -3 Combine like terms: -124.414629365 + -3 = -127.414629365 x = -127.414629365 Simplifying x = -127.414629365Solution
The solution to the problem is based on the solutions from the subproblems. x = {121.414629365, -127.414629365}
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