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Simplifying x2 + -3x + 9x + 13 = 180 Reorder the terms: 13 + -3x + 9x + x2 = 180 Combine like terms: -3x + 9x = 6x 13 + 6x + x2 = 180 Solving 13 + 6x + x2 = 180 Solving for variable 'x'. Reorder the terms: 13 + -180 + 6x + x2 = 180 + -180 Combine like terms: 13 + -180 = -167 -167 + 6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -167 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '167' to each side of the equation. -167 + 6x + 167 + x2 = 0 + 167 Reorder the terms: -167 + 167 + 6x + x2 = 0 + 167 Combine like terms: -167 + 167 = 0 0 + 6x + x2 = 0 + 167 6x + x2 = 0 + 167 Combine like terms: 0 + 167 = 167 6x + x2 = 167 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 167 + 9 Reorder the terms: 9 + 6x + x2 = 167 + 9 Combine like terms: 167 + 9 = 176 9 + 6x + x2 = 176 Factor a perfect square on the left side: (x + 3)(x + 3) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (x + 3) equal to 13.266499161 and -13.266499161.Subproblem 1
x + 3 = 13.266499161 Simplifying x + 3 = 13.266499161 Reorder the terms: 3 + x = 13.266499161 Solving 3 + x = 13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 13.266499161 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.266499161 + -3 x = 13.266499161 + -3 Combine like terms: 13.266499161 + -3 = 10.266499161 x = 10.266499161 Simplifying x = 10.266499161Subproblem 2
x + 3 = -13.266499161 Simplifying x + 3 = -13.266499161 Reorder the terms: 3 + x = -13.266499161 Solving 3 + x = -13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -13.266499161 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.266499161 + -3 x = -13.266499161 + -3 Combine like terms: -13.266499161 + -3 = -16.266499161 x = -16.266499161 Simplifying x = -16.266499161Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.266499161, -16.266499161}
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