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Simplifying x2 + -77x + 196 = 0 Reorder the terms: 196 + -77x + x2 = 0 Solving 196 + -77x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-196' to each side of the equation. 196 + -77x + -196 + x2 = 0 + -196 Reorder the terms: 196 + -196 + -77x + x2 = 0 + -196 Combine like terms: 196 + -196 = 0 0 + -77x + x2 = 0 + -196 -77x + x2 = 0 + -196 Combine like terms: 0 + -196 = -196 -77x + x2 = -196 The x term is -77x. Take half its coefficient (-38.5). Square it (1482.25) and add it to both sides. Add '1482.25' to each side of the equation. -77x + 1482.25 + x2 = -196 + 1482.25 Reorder the terms: 1482.25 + -77x + x2 = -196 + 1482.25 Combine like terms: -196 + 1482.25 = 1286.25 1482.25 + -77x + x2 = 1286.25 Factor a perfect square on the left side: (x + -38.5)(x + -38.5) = 1286.25 Calculate the square root of the right side: 35.864327681 Break this problem into two subproblems by setting (x + -38.5) equal to 35.864327681 and -35.864327681.Subproblem 1
x + -38.5 = 35.864327681 Simplifying x + -38.5 = 35.864327681 Reorder the terms: -38.5 + x = 35.864327681 Solving -38.5 + x = 35.864327681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.5' to each side of the equation. -38.5 + 38.5 + x = 35.864327681 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + x = 35.864327681 + 38.5 x = 35.864327681 + 38.5 Combine like terms: 35.864327681 + 38.5 = 74.364327681 x = 74.364327681 Simplifying x = 74.364327681Subproblem 2
x + -38.5 = -35.864327681 Simplifying x + -38.5 = -35.864327681 Reorder the terms: -38.5 + x = -35.864327681 Solving -38.5 + x = -35.864327681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.5' to each side of the equation. -38.5 + 38.5 + x = -35.864327681 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + x = -35.864327681 + 38.5 x = -35.864327681 + 38.5 Combine like terms: -35.864327681 + 38.5 = 2.635672319 x = 2.635672319 Simplifying x = 2.635672319Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.364327681, 2.635672319}
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