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Simplifying x2 + 24x + -480 = 0 Reorder the terms: -480 + 24x + x2 = 0 Solving -480 + 24x + 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 + 24x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 24x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 24x + x2 = 0 + 480 24x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 24x + x2 = 480 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 480 + 144 Reorder the terms: 144 + 24x + x2 = 480 + 144 Combine like terms: 480 + 144 = 624 144 + 24x + x2 = 624 Factor a perfect square on the left side: (x + 12)(x + 12) = 624 Calculate the square root of the right side: 24.979991994 Break this problem into two subproblems by setting (x + 12) equal to 24.979991994 and -24.979991994.Subproblem 1
x + 12 = 24.979991994 Simplifying x + 12 = 24.979991994 Reorder the terms: 12 + x = 24.979991994 Solving 12 + x = 24.979991994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 24.979991994 + -12 Combine like terms: 12 + -12 = 0 0 + x = 24.979991994 + -12 x = 24.979991994 + -12 Combine like terms: 24.979991994 + -12 = 12.979991994 x = 12.979991994 Simplifying x = 12.979991994Subproblem 2
x + 12 = -24.979991994 Simplifying x + 12 = -24.979991994 Reorder the terms: 12 + x = -24.979991994 Solving 12 + x = -24.979991994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -24.979991994 + -12 Combine like terms: 12 + -12 = 0 0 + x = -24.979991994 + -12 x = -24.979991994 + -12 Combine like terms: -24.979991994 + -12 = -36.979991994 x = -36.979991994 Simplifying x = -36.979991994Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.979991994, -36.979991994}
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