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Simplifying X2 + 22X + -360 = 0 Reorder the terms: -360 + 22X + X2 = 0 Solving -360 + 22X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 22X + 360 + X2 = 0 + 360 Reorder the terms: -360 + 360 + 22X + X2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 22X + X2 = 0 + 360 22X + X2 = 0 + 360 Combine like terms: 0 + 360 = 360 22X + X2 = 360 The X term is 22X. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22X + 121 + X2 = 360 + 121 Reorder the terms: 121 + 22X + X2 = 360 + 121 Combine like terms: 360 + 121 = 481 121 + 22X + X2 = 481 Factor a perfect square on the left side: (X + 11)(X + 11) = 481 Calculate the square root of the right side: 21.931712199 Break this problem into two subproblems by setting (X + 11) equal to 21.931712199 and -21.931712199.Subproblem 1
X + 11 = 21.931712199 Simplifying X + 11 = 21.931712199 Reorder the terms: 11 + X = 21.931712199 Solving 11 + X = 21.931712199 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + X = 21.931712199 + -11 Combine like terms: 11 + -11 = 0 0 + X = 21.931712199 + -11 X = 21.931712199 + -11 Combine like terms: 21.931712199 + -11 = 10.931712199 X = 10.931712199 Simplifying X = 10.931712199Subproblem 2
X + 11 = -21.931712199 Simplifying X + 11 = -21.931712199 Reorder the terms: 11 + X = -21.931712199 Solving 11 + X = -21.931712199 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + X = -21.931712199 + -11 Combine like terms: 11 + -11 = 0 0 + X = -21.931712199 + -11 X = -21.931712199 + -11 Combine like terms: -21.931712199 + -11 = -32.931712199 X = -32.931712199 Simplifying X = -32.931712199Solution
The solution to the problem is based on the solutions from the subproblems. X = {10.931712199, -32.931712199}
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