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Simplifying x2 + 144x + 1265 = 0 Reorder the terms: 1265 + 144x + x2 = 0 Solving 1265 + 144x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1265' to each side of the equation. 1265 + 144x + -1265 + x2 = 0 + -1265 Reorder the terms: 1265 + -1265 + 144x + x2 = 0 + -1265 Combine like terms: 1265 + -1265 = 0 0 + 144x + x2 = 0 + -1265 144x + x2 = 0 + -1265 Combine like terms: 0 + -1265 = -1265 144x + x2 = -1265 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 = -1265 + 5184 Reorder the terms: 5184 + 144x + x2 = -1265 + 5184 Combine like terms: -1265 + 5184 = 3919 5184 + 144x + x2 = 3919 Factor a perfect square on the left side: (x + 72)(x + 72) = 3919 Calculate the square root of the right side: 62.601916904 Break this problem into two subproblems by setting (x + 72) equal to 62.601916904 and -62.601916904.Subproblem 1
x + 72 = 62.601916904 Simplifying x + 72 = 62.601916904 Reorder the terms: 72 + x = 62.601916904 Solving 72 + x = 62.601916904 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 = 62.601916904 + -72 Combine like terms: 72 + -72 = 0 0 + x = 62.601916904 + -72 x = 62.601916904 + -72 Combine like terms: 62.601916904 + -72 = -9.398083096 x = -9.398083096 Simplifying x = -9.398083096Subproblem 2
x + 72 = -62.601916904 Simplifying x + 72 = -62.601916904 Reorder the terms: 72 + x = -62.601916904 Solving 72 + x = -62.601916904 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 = -62.601916904 + -72 Combine like terms: 72 + -72 = 0 0 + x = -62.601916904 + -72 x = -62.601916904 + -72 Combine like terms: -62.601916904 + -72 = -134.601916904 x = -134.601916904 Simplifying x = -134.601916904Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.398083096, -134.601916904}
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