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Simplifying 174 = x(x + -4) Reorder the terms: 174 = x(-4 + x) 174 = (-4 * x + x * x) 174 = (-4x + x2) Solving 174 = -4x + x2 Solving for variable 'x'. Reorder the terms: 174 + 4x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 174 + 4x + -1x2 = 0 + x2 + -1x2 174 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 174 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -174 + -4x + x2 = 0 Move the constant term to the right: Add '174' to each side of the equation. -174 + -4x + 174 + x2 = 0 + 174 Reorder the terms: -174 + 174 + -4x + x2 = 0 + 174 Combine like terms: -174 + 174 = 0 0 + -4x + x2 = 0 + 174 -4x + x2 = 0 + 174 Combine like terms: 0 + 174 = 174 -4x + x2 = 174 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 = 174 + 4 Reorder the terms: 4 + -4x + x2 = 174 + 4 Combine like terms: 174 + 4 = 178 4 + -4x + x2 = 178 Factor a perfect square on the left side: (x + -2)(x + -2) = 178 Calculate the square root of the right side: 13.341664064 Break this problem into two subproblems by setting (x + -2) equal to 13.341664064 and -13.341664064.Subproblem 1
x + -2 = 13.341664064 Simplifying x + -2 = 13.341664064 Reorder the terms: -2 + x = 13.341664064 Solving -2 + x = 13.341664064 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 = 13.341664064 + 2 Combine like terms: -2 + 2 = 0 0 + x = 13.341664064 + 2 x = 13.341664064 + 2 Combine like terms: 13.341664064 + 2 = 15.341664064 x = 15.341664064 Simplifying x = 15.341664064Subproblem 2
x + -2 = -13.341664064 Simplifying x + -2 = -13.341664064 Reorder the terms: -2 + x = -13.341664064 Solving -2 + x = -13.341664064 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 = -13.341664064 + 2 Combine like terms: -2 + 2 = 0 0 + x = -13.341664064 + 2 x = -13.341664064 + 2 Combine like terms: -13.341664064 + 2 = -11.341664064 x = -11.341664064 Simplifying x = -11.341664064Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.341664064, -11.341664064}
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