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Simplifying 2x2 + 19x = 180 Reorder the terms: 19x + 2x2 = 180 Solving 19x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 19x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -90 + 9.5x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 9.5x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 9.5x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 9.5x + x2 = 0 + 90 9.5x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 9.5x + x2 = 90 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 90 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 90 + 22.5625 Combine like terms: 90 + 22.5625 = 112.5625 22.5625 + 9.5x + x2 = 112.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 112.5625 Calculate the square root of the right side: 10.609547587 Break this problem into two subproblems by setting (x + 4.75) equal to 10.609547587 and -10.609547587.Subproblem 1
x + 4.75 = 10.609547587 Simplifying x + 4.75 = 10.609547587 Reorder the terms: 4.75 + x = 10.609547587 Solving 4.75 + x = 10.609547587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 10.609547587 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 10.609547587 + -4.75 x = 10.609547587 + -4.75 Combine like terms: 10.609547587 + -4.75 = 5.859547587 x = 5.859547587 Simplifying x = 5.859547587Subproblem 2
x + 4.75 = -10.609547587 Simplifying x + 4.75 = -10.609547587 Reorder the terms: 4.75 + x = -10.609547587 Solving 4.75 + x = -10.609547587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -10.609547587 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -10.609547587 + -4.75 x = -10.609547587 + -4.75 Combine like terms: -10.609547587 + -4.75 = -15.359547587 x = -15.359547587 Simplifying x = -15.359547587Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.859547587, -15.359547587}
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