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Simplifying x2 + 6x + -624 = 0 Reorder the terms: -624 + 6x + x2 = 0 Solving -624 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '624' to each side of the equation. -624 + 6x + 624 + x2 = 0 + 624 Reorder the terms: -624 + 624 + 6x + x2 = 0 + 624 Combine like terms: -624 + 624 = 0 0 + 6x + x2 = 0 + 624 6x + x2 = 0 + 624 Combine like terms: 0 + 624 = 624 6x + x2 = 624 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 = 624 + 9 Reorder the terms: 9 + 6x + x2 = 624 + 9 Combine like terms: 624 + 9 = 633 9 + 6x + x2 = 633 Factor a perfect square on the left side: (x + 3)(x + 3) = 633 Calculate the square root of the right side: 25.159491251 Break this problem into two subproblems by setting (x + 3) equal to 25.159491251 and -25.159491251.Subproblem 1
x + 3 = 25.159491251 Simplifying x + 3 = 25.159491251 Reorder the terms: 3 + x = 25.159491251 Solving 3 + x = 25.159491251 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 = 25.159491251 + -3 Combine like terms: 3 + -3 = 0 0 + x = 25.159491251 + -3 x = 25.159491251 + -3 Combine like terms: 25.159491251 + -3 = 22.159491251 x = 22.159491251 Simplifying x = 22.159491251Subproblem 2
x + 3 = -25.159491251 Simplifying x + 3 = -25.159491251 Reorder the terms: 3 + x = -25.159491251 Solving 3 + x = -25.159491251 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 = -25.159491251 + -3 Combine like terms: 3 + -3 = 0 0 + x = -25.159491251 + -3 x = -25.159491251 + -3 Combine like terms: -25.159491251 + -3 = -28.159491251 x = -28.159491251 Simplifying x = -28.159491251Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.159491251, -28.159491251}
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