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Simplifying 177 = x(2x + -4) Reorder the terms: 177 = x(-4 + 2x) 177 = (-4 * x + 2x * x) 177 = (-4x + 2x2) Solving 177 = -4x + 2x2 Solving for variable 'x'. Reorder the terms: 177 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2 Combine like terms: -4x + 4x = 0 177 + 4x + -2x2 = 0 + 2x2 + -2x2 177 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 177 + 4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -88.5 + -2x + x2 = 0 Move the constant term to the right: Add '88.5' to each side of the equation. -88.5 + -2x + 88.5 + x2 = 0 + 88.5 Reorder the terms: -88.5 + 88.5 + -2x + x2 = 0 + 88.5 Combine like terms: -88.5 + 88.5 = 0.0 0.0 + -2x + x2 = 0 + 88.5 -2x + x2 = 0 + 88.5 Combine like terms: 0 + 88.5 = 88.5 -2x + x2 = 88.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 88.5 + 1 Reorder the terms: 1 + -2x + x2 = 88.5 + 1 Combine like terms: 88.5 + 1 = 89.5 1 + -2x + x2 = 89.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 89.5 Calculate the square root of the right side: 9.460443964 Break this problem into two subproblems by setting (x + -1) equal to 9.460443964 and -9.460443964.Subproblem 1
x + -1 = 9.460443964 Simplifying x + -1 = 9.460443964 Reorder the terms: -1 + x = 9.460443964 Solving -1 + x = 9.460443964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 9.460443964 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.460443964 + 1 x = 9.460443964 + 1 Combine like terms: 9.460443964 + 1 = 10.460443964 x = 10.460443964 Simplifying x = 10.460443964Subproblem 2
x + -1 = -9.460443964 Simplifying x + -1 = -9.460443964 Reorder the terms: -1 + x = -9.460443964 Solving -1 + x = -9.460443964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -9.460443964 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.460443964 + 1 x = -9.460443964 + 1 Combine like terms: -9.460443964 + 1 = -8.460443964 x = -8.460443964 Simplifying x = -8.460443964Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.460443964, -8.460443964}
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