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Simplifying x(x + 12) + (x + -9) = 180 Reorder the terms: x(12 + x) + (x + -9) = 180 (12 * x + x * x) + (x + -9) = 180 (12x + x2) + (x + -9) = 180 Reorder the terms: 12x + x2 + (-9 + x) = 180 Remove parenthesis around (-9 + x) 12x + x2 + -9 + x = 180 Reorder the terms: -9 + 12x + x + x2 = 180 Combine like terms: 12x + x = 13x -9 + 13x + x2 = 180 Solving -9 + 13x + x2 = 180 Solving for variable 'x'. Reorder the terms: -9 + -180 + 13x + x2 = 180 + -180 Combine like terms: -9 + -180 = -189 -189 + 13x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -189 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '189' to each side of the equation. -189 + 13x + 189 + x2 = 0 + 189 Reorder the terms: -189 + 189 + 13x + x2 = 0 + 189 Combine like terms: -189 + 189 = 0 0 + 13x + x2 = 0 + 189 13x + x2 = 0 + 189 Combine like terms: 0 + 189 = 189 13x + x2 = 189 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 189 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 189 + 42.25 Combine like terms: 189 + 42.25 = 231.25 42.25 + 13x + x2 = 231.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 231.25 Calculate the square root of the right side: 15.206906326 Break this problem into two subproblems by setting (x + 6.5) equal to 15.206906326 and -15.206906326.Subproblem 1
x + 6.5 = 15.206906326 Simplifying x + 6.5 = 15.206906326 Reorder the terms: 6.5 + x = 15.206906326 Solving 6.5 + x = 15.206906326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 15.206906326 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 15.206906326 + -6.5 x = 15.206906326 + -6.5 Combine like terms: 15.206906326 + -6.5 = 8.706906326 x = 8.706906326 Simplifying x = 8.706906326Subproblem 2
x + 6.5 = -15.206906326 Simplifying x + 6.5 = -15.206906326 Reorder the terms: 6.5 + x = -15.206906326 Solving 6.5 + x = -15.206906326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -15.206906326 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -15.206906326 + -6.5 x = -15.206906326 + -6.5 Combine like terms: -15.206906326 + -6.5 = -21.706906326 x = -21.706906326 Simplifying x = -21.706906326Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.706906326, -21.706906326}
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