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Simplifying x2 + 6x + -588 = 0 Reorder the terms: -588 + 6x + x2 = 0 Solving -588 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '588' to each side of the equation. -588 + 6x + 588 + x2 = 0 + 588 Reorder the terms: -588 + 588 + 6x + x2 = 0 + 588 Combine like terms: -588 + 588 = 0 0 + 6x + x2 = 0 + 588 6x + x2 = 0 + 588 Combine like terms: 0 + 588 = 588 6x + x2 = 588 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 = 588 + 9 Reorder the terms: 9 + 6x + x2 = 588 + 9 Combine like terms: 588 + 9 = 597 9 + 6x + x2 = 597 Factor a perfect square on the left side: (x + 3)(x + 3) = 597 Calculate the square root of the right side: 24.433583446 Break this problem into two subproblems by setting (x + 3) equal to 24.433583446 and -24.433583446.Subproblem 1
x + 3 = 24.433583446 Simplifying x + 3 = 24.433583446 Reorder the terms: 3 + x = 24.433583446 Solving 3 + x = 24.433583446 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 = 24.433583446 + -3 Combine like terms: 3 + -3 = 0 0 + x = 24.433583446 + -3 x = 24.433583446 + -3 Combine like terms: 24.433583446 + -3 = 21.433583446 x = 21.433583446 Simplifying x = 21.433583446Subproblem 2
x + 3 = -24.433583446 Simplifying x + 3 = -24.433583446 Reorder the terms: 3 + x = -24.433583446 Solving 3 + x = -24.433583446 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 = -24.433583446 + -3 Combine like terms: 3 + -3 = 0 0 + x = -24.433583446 + -3 x = -24.433583446 + -3 Combine like terms: -24.433583446 + -3 = -27.433583446 x = -27.433583446 Simplifying x = -27.433583446Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.433583446, -27.433583446}
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