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Simplifying 168 = x2 + -4x + 58 Reorder the terms: 168 = 58 + -4x + x2 Solving 168 = 58 + -4x + x2 Solving for variable 'x'. Combine like terms: 168 + -58 = 110 110 + 4x + -1x2 = 58 + -4x + x2 + -58 + 4x + -1x2 Reorder the terms: 110 + 4x + -1x2 = 58 + -58 + -4x + 4x + x2 + -1x2 Combine like terms: 58 + -58 = 0 110 + 4x + -1x2 = 0 + -4x + 4x + x2 + -1x2 110 + 4x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 110 + 4x + -1x2 = 0 + x2 + -1x2 110 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 110 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -110 + -4x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + -4x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + -4x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + -4x + x2 = 0 + 110 -4x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 -4x + x2 = 110 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 = 110 + 4 Reorder the terms: 4 + -4x + x2 = 110 + 4 Combine like terms: 110 + 4 = 114 4 + -4x + x2 = 114 Factor a perfect square on the left side: (x + -2)(x + -2) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x + -2) equal to 10.677078252 and -10.677078252.Subproblem 1
x + -2 = 10.677078252 Simplifying x + -2 = 10.677078252 Reorder the terms: -2 + x = 10.677078252 Solving -2 + x = 10.677078252 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 = 10.677078252 + 2 Combine like terms: -2 + 2 = 0 0 + x = 10.677078252 + 2 x = 10.677078252 + 2 Combine like terms: 10.677078252 + 2 = 12.677078252 x = 12.677078252 Simplifying x = 12.677078252Subproblem 2
x + -2 = -10.677078252 Simplifying x + -2 = -10.677078252 Reorder the terms: -2 + x = -10.677078252 Solving -2 + x = -10.677078252 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 = -10.677078252 + 2 Combine like terms: -2 + 2 = 0 0 + x = -10.677078252 + 2 x = -10.677078252 + 2 Combine like terms: -10.677078252 + 2 = -8.677078252 x = -8.677078252 Simplifying x = -8.677078252Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.677078252, -8.677078252}
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