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Simplifying 180 = x2 + 20 + 4x Reorder the terms: 180 = 20 + 4x + x2 Solving 180 = 20 + 4x + x2 Solving for variable 'x'. Combine like terms: 180 + -20 = 160 160 + -4x + -1x2 = 20 + 4x + x2 + -20 + -4x + -1x2 Reorder the terms: 160 + -4x + -1x2 = 20 + -20 + 4x + -4x + x2 + -1x2 Combine like terms: 20 + -20 = 0 160 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2 160 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 160 + -4x + -1x2 = 0 + x2 + -1x2 160 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 160 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -160 + 4x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + 4x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 4x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 4x + x2 = 0 + 160 4x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 4x + x2 = 160 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 = 160 + 4 Reorder the terms: 4 + 4x + x2 = 160 + 4 Combine like terms: 160 + 4 = 164 4 + 4x + x2 = 164 Factor a perfect square on the left side: (x + 2)(x + 2) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (x + 2) equal to 12.806248475 and -12.806248475.Subproblem 1
x + 2 = 12.806248475 Simplifying x + 2 = 12.806248475 Reorder the terms: 2 + x = 12.806248475 Solving 2 + x = 12.806248475 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 = 12.806248475 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.806248475 + -2 x = 12.806248475 + -2 Combine like terms: 12.806248475 + -2 = 10.806248475 x = 10.806248475 Simplifying x = 10.806248475Subproblem 2
x + 2 = -12.806248475 Simplifying x + 2 = -12.806248475 Reorder the terms: 2 + x = -12.806248475 Solving 2 + x = -12.806248475 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 = -12.806248475 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.806248475 + -2 x = -12.806248475 + -2 Combine like terms: -12.806248475 + -2 = -14.806248475 x = -14.806248475 Simplifying x = -14.806248475Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.806248475, -14.806248475}
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