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Simplifying x2 + 16x + -78 = 0 Reorder the terms: -78 + 16x + x2 = 0 Solving -78 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + 16x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + 16x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 16x + x2 = 0 + 78 16x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 16x + x2 = 78 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 = 78 + 64 Reorder the terms: 64 + 16x + x2 = 78 + 64 Combine like terms: 78 + 64 = 142 64 + 16x + x2 = 142 Factor a perfect square on the left side: (x + 8)(x + 8) = 142 Calculate the square root of the right side: 11.916375288 Break this problem into two subproblems by setting (x + 8) equal to 11.916375288 and -11.916375288.Subproblem 1
x + 8 = 11.916375288 Simplifying x + 8 = 11.916375288 Reorder the terms: 8 + x = 11.916375288 Solving 8 + x = 11.916375288 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 = 11.916375288 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.916375288 + -8 x = 11.916375288 + -8 Combine like terms: 11.916375288 + -8 = 3.916375288 x = 3.916375288 Simplifying x = 3.916375288Subproblem 2
x + 8 = -11.916375288 Simplifying x + 8 = -11.916375288 Reorder the terms: 8 + x = -11.916375288 Solving 8 + x = -11.916375288 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 = -11.916375288 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.916375288 + -8 x = -11.916375288 + -8 Combine like terms: -11.916375288 + -8 = -19.916375288 x = -19.916375288 Simplifying x = -19.916375288Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.916375288, -19.916375288}
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