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Simplifying x2 + -78x + -116 = 0 Reorder the terms: -116 + -78x + x2 = 0 Solving -116 + -78x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '116' to each side of the equation. -116 + -78x + 116 + x2 = 0 + 116 Reorder the terms: -116 + 116 + -78x + x2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + -78x + x2 = 0 + 116 -78x + x2 = 0 + 116 Combine like terms: 0 + 116 = 116 -78x + x2 = 116 The x term is -78x. Take half its coefficient (-39). Square it (1521) and add it to both sides. Add '1521' to each side of the equation. -78x + 1521 + x2 = 116 + 1521 Reorder the terms: 1521 + -78x + x2 = 116 + 1521 Combine like terms: 116 + 1521 = 1637 1521 + -78x + x2 = 1637 Factor a perfect square on the left side: (x + -39)(x + -39) = 1637 Calculate the square root of the right side: 40.459856648 Break this problem into two subproblems by setting (x + -39) equal to 40.459856648 and -40.459856648.Subproblem 1
x + -39 = 40.459856648 Simplifying x + -39 = 40.459856648 Reorder the terms: -39 + x = 40.459856648 Solving -39 + x = 40.459856648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + x = 40.459856648 + 39 Combine like terms: -39 + 39 = 0 0 + x = 40.459856648 + 39 x = 40.459856648 + 39 Combine like terms: 40.459856648 + 39 = 79.459856648 x = 79.459856648 Simplifying x = 79.459856648Subproblem 2
x + -39 = -40.459856648 Simplifying x + -39 = -40.459856648 Reorder the terms: -39 + x = -40.459856648 Solving -39 + x = -40.459856648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + x = -40.459856648 + 39 Combine like terms: -39 + 39 = 0 0 + x = -40.459856648 + 39 x = -40.459856648 + 39 Combine like terms: -40.459856648 + 39 = -1.459856648 x = -1.459856648 Simplifying x = -1.459856648Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.459856648, -1.459856648}
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