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Simplifying x2 + -16x + -9740 = 0 Reorder the terms: -9740 + -16x + x2 = 0 Solving -9740 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9740' to each side of the equation. -9740 + -16x + 9740 + x2 = 0 + 9740 Reorder the terms: -9740 + 9740 + -16x + x2 = 0 + 9740 Combine like terms: -9740 + 9740 = 0 0 + -16x + x2 = 0 + 9740 -16x + x2 = 0 + 9740 Combine like terms: 0 + 9740 = 9740 -16x + x2 = 9740 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 9740 + 64 Reorder the terms: 64 + -16x + x2 = 9740 + 64 Combine like terms: 9740 + 64 = 9804 64 + -16x + x2 = 9804 Factor a perfect square on the left side: (x + -8)(x + -8) = 9804 Calculate the square root of the right side: 99.015150356 Break this problem into two subproblems by setting (x + -8) equal to 99.015150356 and -99.015150356.Subproblem 1
x + -8 = 99.015150356 Simplifying x + -8 = 99.015150356 Reorder the terms: -8 + x = 99.015150356 Solving -8 + x = 99.015150356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 99.015150356 + 8 Combine like terms: -8 + 8 = 0 0 + x = 99.015150356 + 8 x = 99.015150356 + 8 Combine like terms: 99.015150356 + 8 = 107.015150356 x = 107.015150356 Simplifying x = 107.015150356Subproblem 2
x + -8 = -99.015150356 Simplifying x + -8 = -99.015150356 Reorder the terms: -8 + x = -99.015150356 Solving -8 + x = -99.015150356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -99.015150356 + 8 Combine like terms: -8 + 8 = 0 0 + x = -99.015150356 + 8 x = -99.015150356 + 8 Combine like terms: -99.015150356 + 8 = -91.015150356 x = -91.015150356 Simplifying x = -91.015150356Solution
The solution to the problem is based on the solutions from the subproblems. x = {107.015150356, -91.015150356}
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