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Simplifying x2 + 144 = 49x Reorder the terms: 144 + x2 = 49x Solving 144 + x2 = 49x Solving for variable 'x'. Reorder the terms: 144 + -49x + x2 = 49x + -49x Combine like terms: 49x + -49x = 0 144 + -49x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-144' to each side of the equation. 144 + -49x + -144 + x2 = 0 + -144 Reorder the terms: 144 + -144 + -49x + x2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -49x + x2 = 0 + -144 -49x + x2 = 0 + -144 Combine like terms: 0 + -144 = -144 -49x + x2 = -144 The x term is -49x. Take half its coefficient (-24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. -49x + 600.25 + x2 = -144 + 600.25 Reorder the terms: 600.25 + -49x + x2 = -144 + 600.25 Combine like terms: -144 + 600.25 = 456.25 600.25 + -49x + x2 = 456.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 456.25 Calculate the square root of the right side: 21.360009363 Break this problem into two subproblems by setting (x + -24.5) equal to 21.360009363 and -21.360009363.Subproblem 1
x + -24.5 = 21.360009363 Simplifying x + -24.5 = 21.360009363 Reorder the terms: -24.5 + x = 21.360009363 Solving -24.5 + x = 21.360009363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = 21.360009363 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 21.360009363 + 24.5 x = 21.360009363 + 24.5 Combine like terms: 21.360009363 + 24.5 = 45.860009363 x = 45.860009363 Simplifying x = 45.860009363Subproblem 2
x + -24.5 = -21.360009363 Simplifying x + -24.5 = -21.360009363 Reorder the terms: -24.5 + x = -21.360009363 Solving -24.5 + x = -21.360009363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = -21.360009363 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -21.360009363 + 24.5 x = -21.360009363 + 24.5 Combine like terms: -21.360009363 + 24.5 = 3.139990637 x = 3.139990637 Simplifying x = 3.139990637Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.860009363, 3.139990637}
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