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Simplifying 180 = 52 + 5x + 30 + 180 + -3x2 + 4 Reorder the terms: 180 = 52 + 30 + 180 + 4 + 5x + -3x2 Combine like terms: 52 + 30 = 82 180 = 82 + 180 + 4 + 5x + -3x2 Combine like terms: 82 + 180 = 262 180 = 262 + 4 + 5x + -3x2 Combine like terms: 262 + 4 = 266 180 = 266 + 5x + -3x2 Solving 180 = 266 + 5x + -3x2 Solving for variable 'x'. Combine like terms: 180 + -266 = -86 -86 + -5x + 3x2 = 266 + 5x + -3x2 + -266 + -5x + 3x2 Reorder the terms: -86 + -5x + 3x2 = 266 + -266 + 5x + -5x + -3x2 + 3x2 Combine like terms: 266 + -266 = 0 -86 + -5x + 3x2 = 0 + 5x + -5x + -3x2 + 3x2 -86 + -5x + 3x2 = 5x + -5x + -3x2 + 3x2 Combine like terms: 5x + -5x = 0 -86 + -5x + 3x2 = 0 + -3x2 + 3x2 -86 + -5x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -86 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -28.66666667 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '28.66666667' to each side of the equation. -28.66666667 + -1.666666667x + 28.66666667 + x2 = 0 + 28.66666667 Reorder the terms: -28.66666667 + 28.66666667 + -1.666666667x + x2 = 0 + 28.66666667 Combine like terms: -28.66666667 + 28.66666667 = 0.00000000 0.00000000 + -1.666666667x + x2 = 0 + 28.66666667 -1.666666667x + x2 = 0 + 28.66666667 Combine like terms: 0 + 28.66666667 = 28.66666667 -1.666666667x + x2 = 28.66666667 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 28.66666667 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 28.66666667 + 0.6944444447 Combine like terms: 28.66666667 + 0.6944444447 = 29.3611111147 0.6944444447 + -1.666666667x + x2 = 29.3611111147 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 29.3611111147 Calculate the square root of the right side: 5.418589403 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 5.418589403 and -5.418589403.Subproblem 1
x + -0.8333333335 = 5.418589403 Simplifying x + -0.8333333335 = 5.418589403 Reorder the terms: -0.8333333335 + x = 5.418589403 Solving -0.8333333335 + x = 5.418589403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 5.418589403 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 5.418589403 + 0.8333333335 x = 5.418589403 + 0.8333333335 Combine like terms: 5.418589403 + 0.8333333335 = 6.2519227365 x = 6.2519227365 Simplifying x = 6.2519227365Subproblem 2
x + -0.8333333335 = -5.418589403 Simplifying x + -0.8333333335 = -5.418589403 Reorder the terms: -0.8333333335 + x = -5.418589403 Solving -0.8333333335 + x = -5.418589403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -5.418589403 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -5.418589403 + 0.8333333335 x = -5.418589403 + 0.8333333335 Combine like terms: -5.418589403 + 0.8333333335 = -4.5852560695 x = -4.5852560695 Simplifying x = -4.5852560695Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.2519227365, -4.5852560695}
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