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Simplifying x2 + 6x + -480 = 0 Reorder the terms: -480 + 6x + x2 = 0 Solving -480 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '480' to each side of the equation. -480 + 6x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 6x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 6x + x2 = 0 + 480 6x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 6x + x2 = 480 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 = 480 + 9 Reorder the terms: 9 + 6x + x2 = 480 + 9 Combine like terms: 480 + 9 = 489 9 + 6x + x2 = 489 Factor a perfect square on the left side: (x + 3)(x + 3) = 489 Calculate the square root of the right side: 22.113344387 Break this problem into two subproblems by setting (x + 3) equal to 22.113344387 and -22.113344387.Subproblem 1
x + 3 = 22.113344387 Simplifying x + 3 = 22.113344387 Reorder the terms: 3 + x = 22.113344387 Solving 3 + x = 22.113344387 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 = 22.113344387 + -3 Combine like terms: 3 + -3 = 0 0 + x = 22.113344387 + -3 x = 22.113344387 + -3 Combine like terms: 22.113344387 + -3 = 19.113344387 x = 19.113344387 Simplifying x = 19.113344387Subproblem 2
x + 3 = -22.113344387 Simplifying x + 3 = -22.113344387 Reorder the terms: 3 + x = -22.113344387 Solving 3 + x = -22.113344387 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 = -22.113344387 + -3 Combine like terms: 3 + -3 = 0 0 + x = -22.113344387 + -3 x = -22.113344387 + -3 Combine like terms: -22.113344387 + -3 = -25.113344387 x = -25.113344387 Simplifying x = -25.113344387Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.113344387, -25.113344387}
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