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Simplifying 0.5x((x + 3) + (x + 7)) + -225 = 0 Reorder the terms: 0.5x((3 + x) + (x + 7)) + -225 = 0 Remove parenthesis around (3 + x) 0.5x(3 + x + (x + 7)) + -225 = 0 Reorder the terms: 0.5x(3 + x + (7 + x)) + -225 = 0 Remove parenthesis around (7 + x) 0.5x(3 + x + 7 + x) + -225 = 0 Reorder the terms: 0.5x(3 + 7 + x + x) + -225 = 0 Combine like terms: 3 + 7 = 10 0.5x(10 + x + x) + -225 = 0 Combine like terms: x + x = 2x 0.5x(10 + 2x) + -225 = 0 (10 * 0.5x + 2x * 0.5x) + -225 = 0 (5x + 1x2) + -225 = 0 Reorder the terms: -225 + 5x + 1x2 = 0 Solving -225 + 5x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 5x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 5x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 5x + x2 = 0 + 225 5x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 5x + x2 = 225 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 225 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 225 + 6.25 Combine like terms: 225 + 6.25 = 231.25 6.25 + 5x + x2 = 231.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 231.25 Calculate the square root of the right side: 15.206906326 Break this problem into two subproblems by setting (x + 2.5) equal to 15.206906326 and -15.206906326.Subproblem 1
x + 2.5 = 15.206906326 Simplifying x + 2.5 = 15.206906326 Reorder the terms: 2.5 + x = 15.206906326 Solving 2.5 + x = 15.206906326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 15.206906326 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 15.206906326 + -2.5 x = 15.206906326 + -2.5 Combine like terms: 15.206906326 + -2.5 = 12.706906326 x = 12.706906326 Simplifying x = 12.706906326Subproblem 2
x + 2.5 = -15.206906326 Simplifying x + 2.5 = -15.206906326 Reorder the terms: 2.5 + x = -15.206906326 Solving 2.5 + x = -15.206906326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -15.206906326 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -15.206906326 + -2.5 x = -15.206906326 + -2.5 Combine like terms: -15.206906326 + -2.5 = -17.706906326 x = -17.706906326 Simplifying x = -17.706906326Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.706906326, -17.706906326}
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