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Simplifying x2 + 6x = 576 Reorder the terms: 6x + x2 = 576 Solving 6x + x2 = 576 Solving for variable 'x'. Reorder the terms: -576 + 6x + x2 = 576 + -576 Combine like terms: 576 + -576 = 0 -576 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '576' to each side of the equation. -576 + 6x + 576 + x2 = 0 + 576 Reorder the terms: -576 + 576 + 6x + x2 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + 6x + x2 = 0 + 576 6x + x2 = 0 + 576 Combine like terms: 0 + 576 = 576 6x + x2 = 576 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 = 576 + 9 Reorder the terms: 9 + 6x + x2 = 576 + 9 Combine like terms: 576 + 9 = 585 9 + 6x + x2 = 585 Factor a perfect square on the left side: (x + 3)(x + 3) = 585 Calculate the square root of the right side: 24.186773245 Break this problem into two subproblems by setting (x + 3) equal to 24.186773245 and -24.186773245.Subproblem 1
x + 3 = 24.186773245 Simplifying x + 3 = 24.186773245 Reorder the terms: 3 + x = 24.186773245 Solving 3 + x = 24.186773245 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 = 24.186773245 + -3 Combine like terms: 3 + -3 = 0 0 + x = 24.186773245 + -3 x = 24.186773245 + -3 Combine like terms: 24.186773245 + -3 = 21.186773245 x = 21.186773245 Simplifying x = 21.186773245Subproblem 2
x + 3 = -24.186773245 Simplifying x + 3 = -24.186773245 Reorder the terms: 3 + x = -24.186773245 Solving 3 + x = -24.186773245 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 = -24.186773245 + -3 Combine like terms: 3 + -3 = 0 0 + x = -24.186773245 + -3 x = -24.186773245 + -3 Combine like terms: -24.186773245 + -3 = -27.186773245 x = -27.186773245 Simplifying x = -27.186773245Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.186773245, -27.186773245}
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