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Simplifying x2 + -144x + 384 = 0 Reorder the terms: 384 + -144x + x2 = 0 Solving 384 + -144x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-384' to each side of the equation. 384 + -144x + -384 + x2 = 0 + -384 Reorder the terms: 384 + -384 + -144x + x2 = 0 + -384 Combine like terms: 384 + -384 = 0 0 + -144x + x2 = 0 + -384 -144x + x2 = 0 + -384 Combine like terms: 0 + -384 = -384 -144x + x2 = -384 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 = -384 + 5184 Reorder the terms: 5184 + -144x + x2 = -384 + 5184 Combine like terms: -384 + 5184 = 4800 5184 + -144x + x2 = 4800 Factor a perfect square on the left side: (x + -72)(x + -72) = 4800 Calculate the square root of the right side: 69.282032303 Break this problem into two subproblems by setting (x + -72) equal to 69.282032303 and -69.282032303.Subproblem 1
x + -72 = 69.282032303 Simplifying x + -72 = 69.282032303 Reorder the terms: -72 + x = 69.282032303 Solving -72 + x = 69.282032303 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 = 69.282032303 + 72 Combine like terms: -72 + 72 = 0 0 + x = 69.282032303 + 72 x = 69.282032303 + 72 Combine like terms: 69.282032303 + 72 = 141.282032303 x = 141.282032303 Simplifying x = 141.282032303Subproblem 2
x + -72 = -69.282032303 Simplifying x + -72 = -69.282032303 Reorder the terms: -72 + x = -69.282032303 Solving -72 + x = -69.282032303 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 = -69.282032303 + 72 Combine like terms: -72 + 72 = 0 0 + x = -69.282032303 + 72 x = -69.282032303 + 72 Combine like terms: -69.282032303 + 72 = 2.717967697 x = 2.717967697 Simplifying x = 2.717967697Solution
The solution to the problem is based on the solutions from the subproblems. x = {141.282032303, 2.717967697}
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