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Simplifying x2 + -30x + -144 = 0 Reorder the terms: -144 + -30x + x2 = 0 Solving -144 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -30x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -30x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -30x + x2 = 0 + 144 -30x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -30x + x2 = 144 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 144 + 225 Reorder the terms: 225 + -30x + x2 = 144 + 225 Combine like terms: 144 + 225 = 369 225 + -30x + x2 = 369 Factor a perfect square on the left side: (x + -15)(x + -15) = 369 Calculate the square root of the right side: 19.209372712 Break this problem into two subproblems by setting (x + -15) equal to 19.209372712 and -19.209372712.Subproblem 1
x + -15 = 19.209372712 Simplifying x + -15 = 19.209372712 Reorder the terms: -15 + x = 19.209372712 Solving -15 + x = 19.209372712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 19.209372712 + 15 Combine like terms: -15 + 15 = 0 0 + x = 19.209372712 + 15 x = 19.209372712 + 15 Combine like terms: 19.209372712 + 15 = 34.209372712 x = 34.209372712 Simplifying x = 34.209372712Subproblem 2
x + -15 = -19.209372712 Simplifying x + -15 = -19.209372712 Reorder the terms: -15 + x = -19.209372712 Solving -15 + x = -19.209372712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -19.209372712 + 15 Combine like terms: -15 + 15 = 0 0 + x = -19.209372712 + 15 x = -19.209372712 + 15 Combine like terms: -19.209372712 + 15 = -4.209372712 x = -4.209372712 Simplifying x = -4.209372712Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.209372712, -4.209372712}
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