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Simplifying -4x + 1.8x2 = 180 Solving -4x + 1.8x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -4x + 1.8x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -4x + 1.8x2 = 0 Begin completing the square. Divide all terms by 1.8 the coefficient of the squared term: Divide each side by '1.8'. -100 + -2.222222222x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -2.222222222x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -2.222222222x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -2.222222222x + x2 = 0 + 100 -2.222222222x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -2.222222222x + x2 = 100 The x term is -2.222222222x. Take half its coefficient (-1.111111111). Square it (1.234567901) and add it to both sides. Add '1.234567901' to each side of the equation. -2.222222222x + 1.234567901 + x2 = 100 + 1.234567901 Reorder the terms: 1.234567901 + -2.222222222x + x2 = 100 + 1.234567901 Combine like terms: 100 + 1.234567901 = 101.234567901 1.234567901 + -2.222222222x + x2 = 101.234567901 Factor a perfect square on the left side: (x + -1.111111111)(x + -1.111111111) = 101.234567901 Calculate the square root of the right side: 10.061539042 Break this problem into two subproblems by setting (x + -1.111111111) equal to 10.061539042 and -10.061539042.Subproblem 1
x + -1.111111111 = 10.061539042 Simplifying x + -1.111111111 = 10.061539042 Reorder the terms: -1.111111111 + x = 10.061539042 Solving -1.111111111 + x = 10.061539042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.111111111' to each side of the equation. -1.111111111 + 1.111111111 + x = 10.061539042 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = 10.061539042 + 1.111111111 x = 10.061539042 + 1.111111111 Combine like terms: 10.061539042 + 1.111111111 = 11.172650153 x = 11.172650153 Simplifying x = 11.172650153Subproblem 2
x + -1.111111111 = -10.061539042 Simplifying x + -1.111111111 = -10.061539042 Reorder the terms: -1.111111111 + x = -10.061539042 Solving -1.111111111 + x = -10.061539042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.111111111' to each side of the equation. -1.111111111 + 1.111111111 + x = -10.061539042 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = -10.061539042 + 1.111111111 x = -10.061539042 + 1.111111111 Combine like terms: -10.061539042 + 1.111111111 = -8.950427931 x = -8.950427931 Simplifying x = -8.950427931Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.172650153, -8.950427931}
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