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Simplifying x2 + -16x + -99 = 60 Reorder the terms: -99 + -16x + x2 = 60 Solving -99 + -16x + x2 = 60 Solving for variable 'x'. Reorder the terms: -99 + -60 + -16x + x2 = 60 + -60 Combine like terms: -99 + -60 = -159 -159 + -16x + x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -159 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '159' to each side of the equation. -159 + -16x + 159 + x2 = 0 + 159 Reorder the terms: -159 + 159 + -16x + x2 = 0 + 159 Combine like terms: -159 + 159 = 0 0 + -16x + x2 = 0 + 159 -16x + x2 = 0 + 159 Combine like terms: 0 + 159 = 159 -16x + x2 = 159 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 = 159 + 64 Reorder the terms: 64 + -16x + x2 = 159 + 64 Combine like terms: 159 + 64 = 223 64 + -16x + x2 = 223 Factor a perfect square on the left side: (x + -8)(x + -8) = 223 Calculate the square root of the right side: 14.933184523 Break this problem into two subproblems by setting (x + -8) equal to 14.933184523 and -14.933184523.Subproblem 1
x + -8 = 14.933184523 Simplifying x + -8 = 14.933184523 Reorder the terms: -8 + x = 14.933184523 Solving -8 + x = 14.933184523 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 = 14.933184523 + 8 Combine like terms: -8 + 8 = 0 0 + x = 14.933184523 + 8 x = 14.933184523 + 8 Combine like terms: 14.933184523 + 8 = 22.933184523 x = 22.933184523 Simplifying x = 22.933184523Subproblem 2
x + -8 = -14.933184523 Simplifying x + -8 = -14.933184523 Reorder the terms: -8 + x = -14.933184523 Solving -8 + x = -14.933184523 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 = -14.933184523 + 8 Combine like terms: -8 + 8 = 0 0 + x = -14.933184523 + 8 x = -14.933184523 + 8 Combine like terms: -14.933184523 + 8 = -6.933184523 x = -6.933184523 Simplifying x = -6.933184523Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.933184523, -6.933184523}
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