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Simplifying 3x + 2x(x + 12) + (2x + 4) = 360 Reorder the terms: 3x + 2x(12 + x) + (2x + 4) = 360 3x + (12 * 2x + x * 2x) + (2x + 4) = 360 3x + (24x + 2x2) + (2x + 4) = 360 Reorder the terms: 3x + 24x + 2x2 + (4 + 2x) = 360 Remove parenthesis around (4 + 2x) 3x + 24x + 2x2 + 4 + 2x = 360 Reorder the terms: 4 + 3x + 24x + 2x + 2x2 = 360 Combine like terms: 3x + 24x = 27x 4 + 27x + 2x + 2x2 = 360 Combine like terms: 27x + 2x = 29x 4 + 29x + 2x2 = 360 Solving 4 + 29x + 2x2 = 360 Solving for variable 'x'. Reorder the terms: 4 + -360 + 29x + 2x2 = 360 + -360 Combine like terms: 4 + -360 = -356 -356 + 29x + 2x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -356 + 29x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -178 + 14.5x + x2 = 0 Move the constant term to the right: Add '178' to each side of the equation. -178 + 14.5x + 178 + x2 = 0 + 178 Reorder the terms: -178 + 178 + 14.5x + x2 = 0 + 178 Combine like terms: -178 + 178 = 0 0 + 14.5x + x2 = 0 + 178 14.5x + x2 = 0 + 178 Combine like terms: 0 + 178 = 178 14.5x + x2 = 178 The x term is 14.5x. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5x + 52.5625 + x2 = 178 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = 178 + 52.5625 Combine like terms: 178 + 52.5625 = 230.5625 52.5625 + 14.5x + x2 = 230.5625 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = 230.5625 Calculate the square root of the right side: 15.184284639 Break this problem into two subproblems by setting (x + 7.25) equal to 15.184284639 and -15.184284639.Subproblem 1
x + 7.25 = 15.184284639 Simplifying x + 7.25 = 15.184284639 Reorder the terms: 7.25 + x = 15.184284639 Solving 7.25 + x = 15.184284639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 15.184284639 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 15.184284639 + -7.25 x = 15.184284639 + -7.25 Combine like terms: 15.184284639 + -7.25 = 7.934284639 x = 7.934284639 Simplifying x = 7.934284639Subproblem 2
x + 7.25 = -15.184284639 Simplifying x + 7.25 = -15.184284639 Reorder the terms: 7.25 + x = -15.184284639 Solving 7.25 + x = -15.184284639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -15.184284639 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -15.184284639 + -7.25 x = -15.184284639 + -7.25 Combine like terms: -15.184284639 + -7.25 = -22.434284639 x = -22.434284639 Simplifying x = -22.434284639Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.934284639, -22.434284639}
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