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Simplifying x2 + 144x + 864 = 0 Reorder the terms: 864 + 144x + x2 = 0 Solving 864 + 144x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-864' to each side of the equation. 864 + 144x + -864 + x2 = 0 + -864 Reorder the terms: 864 + -864 + 144x + x2 = 0 + -864 Combine like terms: 864 + -864 = 0 0 + 144x + x2 = 0 + -864 144x + x2 = 0 + -864 Combine like terms: 0 + -864 = -864 144x + x2 = -864 The x term is 144x. Take half its coefficient (72). Square it (5184) and add it to both sides. Add '5184' to each side of the equation. 144x + 5184 + x2 = -864 + 5184 Reorder the terms: 5184 + 144x + x2 = -864 + 5184 Combine like terms: -864 + 5184 = 4320 5184 + 144x + x2 = 4320 Factor a perfect square on the left side: (x + 72)(x + 72) = 4320 Calculate the square root of the right side: 65.726706901 Break this problem into two subproblems by setting (x + 72) equal to 65.726706901 and -65.726706901.Subproblem 1
x + 72 = 65.726706901 Simplifying x + 72 = 65.726706901 Reorder the terms: 72 + x = 65.726706901 Solving 72 + x = 65.726706901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-72' to each side of the equation. 72 + -72 + x = 65.726706901 + -72 Combine like terms: 72 + -72 = 0 0 + x = 65.726706901 + -72 x = 65.726706901 + -72 Combine like terms: 65.726706901 + -72 = -6.273293099 x = -6.273293099 Simplifying x = -6.273293099Subproblem 2
x + 72 = -65.726706901 Simplifying x + 72 = -65.726706901 Reorder the terms: 72 + x = -65.726706901 Solving 72 + x = -65.726706901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-72' to each side of the equation. 72 + -72 + x = -65.726706901 + -72 Combine like terms: 72 + -72 = 0 0 + x = -65.726706901 + -72 x = -65.726706901 + -72 Combine like terms: -65.726706901 + -72 = -137.726706901 x = -137.726706901 Simplifying x = -137.726706901Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.273293099, -137.726706901}
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