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Simplifying 176 = x2 + 4x Reorder the terms: 176 = 4x + x2 Solving 176 = 4x + x2 Solving for variable 'x'. Reorder the terms: 176 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 176 + -4x + -1x2 = 0 + x2 + -1x2 176 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 176 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -176 + 4x + x2 = 0 Move the constant term to the right: Add '176' to each side of the equation. -176 + 4x + 176 + x2 = 0 + 176 Reorder the terms: -176 + 176 + 4x + x2 = 0 + 176 Combine like terms: -176 + 176 = 0 0 + 4x + x2 = 0 + 176 4x + x2 = 0 + 176 Combine like terms: 0 + 176 = 176 4x + x2 = 176 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 = 176 + 4 Reorder the terms: 4 + 4x + x2 = 176 + 4 Combine like terms: 176 + 4 = 180 4 + 4x + x2 = 180 Factor a perfect square on the left side: (x + 2)(x + 2) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (x + 2) equal to 13.416407865 and -13.416407865.Subproblem 1
x + 2 = 13.416407865 Simplifying x + 2 = 13.416407865 Reorder the terms: 2 + x = 13.416407865 Solving 2 + x = 13.416407865 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 = 13.416407865 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.416407865 + -2 x = 13.416407865 + -2 Combine like terms: 13.416407865 + -2 = 11.416407865 x = 11.416407865 Simplifying x = 11.416407865Subproblem 2
x + 2 = -13.416407865 Simplifying x + 2 = -13.416407865 Reorder the terms: 2 + x = -13.416407865 Solving 2 + x = -13.416407865 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 = -13.416407865 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.416407865 + -2 x = -13.416407865 + -2 Combine like terms: -13.416407865 + -2 = -15.416407865 x = -15.416407865 Simplifying x = -15.416407865Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.416407865, -15.416407865}
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