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Simplifying 0 = x2 + -4x + -168 Reorder the terms: 0 = -168 + -4x + x2 Solving 0 = -168 + -4x + x2 Solving for variable 'x'. Combine like terms: 0 + 168 = 168 168 + 4x + -1x2 = -168 + -4x + x2 + 168 + 4x + -1x2 Reorder the terms: 168 + 4x + -1x2 = -168 + 168 + -4x + 4x + x2 + -1x2 Combine like terms: -168 + 168 = 0 168 + 4x + -1x2 = 0 + -4x + 4x + x2 + -1x2 168 + 4x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 168 + 4x + -1x2 = 0 + x2 + -1x2 168 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 168 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -168 + -4x + x2 = 0 Move the constant term to the right: Add '168' to each side of the equation. -168 + -4x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + -4x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + -4x + x2 = 0 + 168 -4x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 -4x + x2 = 168 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 = 168 + 4 Reorder the terms: 4 + -4x + x2 = 168 + 4 Combine like terms: 168 + 4 = 172 4 + -4x + x2 = 172 Factor a perfect square on the left side: (x + -2)(x + -2) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (x + -2) equal to 13.114877049 and -13.114877049.Subproblem 1
x + -2 = 13.114877049 Simplifying x + -2 = 13.114877049 Reorder the terms: -2 + x = 13.114877049 Solving -2 + x = 13.114877049 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 = 13.114877049 + 2 Combine like terms: -2 + 2 = 0 0 + x = 13.114877049 + 2 x = 13.114877049 + 2 Combine like terms: 13.114877049 + 2 = 15.114877049 x = 15.114877049 Simplifying x = 15.114877049Subproblem 2
x + -2 = -13.114877049 Simplifying x + -2 = -13.114877049 Reorder the terms: -2 + x = -13.114877049 Solving -2 + x = -13.114877049 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 = -13.114877049 + 2 Combine like terms: -2 + 2 = 0 0 + x = -13.114877049 + 2 x = -13.114877049 + 2 Combine like terms: -13.114877049 + 2 = -11.114877049 x = -11.114877049 Simplifying x = -11.114877049Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.114877049, -11.114877049}
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