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Simplifying x2 + -4x + 16 = 169 Reorder the terms: 16 + -4x + x2 = 169 Solving 16 + -4x + x2 = 169 Solving for variable 'x'. Reorder the terms: 16 + -169 + -4x + x2 = 169 + -169 Combine like terms: 16 + -169 = -153 -153 + -4x + x2 = 169 + -169 Combine like terms: 169 + -169 = 0 -153 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '153' to each side of the equation. -153 + -4x + 153 + x2 = 0 + 153 Reorder the terms: -153 + 153 + -4x + x2 = 0 + 153 Combine like terms: -153 + 153 = 0 0 + -4x + x2 = 0 + 153 -4x + x2 = 0 + 153 Combine like terms: 0 + 153 = 153 -4x + x2 = 153 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 153 + 4 Reorder the terms: 4 + -4x + x2 = 153 + 4 Combine like terms: 153 + 4 = 157 4 + -4x + x2 = 157 Factor a perfect square on the left side: (x + -2)(x + -2) = 157 Calculate the square root of the right side: 12.529964086 Break this problem into two subproblems by setting (x + -2) equal to 12.529964086 and -12.529964086.Subproblem 1
x + -2 = 12.529964086 Simplifying x + -2 = 12.529964086 Reorder the terms: -2 + x = 12.529964086 Solving -2 + x = 12.529964086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 12.529964086 + 2 Combine like terms: -2 + 2 = 0 0 + x = 12.529964086 + 2 x = 12.529964086 + 2 Combine like terms: 12.529964086 + 2 = 14.529964086 x = 14.529964086 Simplifying x = 14.529964086Subproblem 2
x + -2 = -12.529964086 Simplifying x + -2 = -12.529964086 Reorder the terms: -2 + x = -12.529964086 Solving -2 + x = -12.529964086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -12.529964086 + 2 Combine like terms: -2 + 2 = 0 0 + x = -12.529964086 + 2 x = -12.529964086 + 2 Combine like terms: -12.529964086 + 2 = -10.529964086 x = -10.529964086 Simplifying x = -10.529964086Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.529964086, -10.529964086}
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