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Simplifying x2 + -30x + 49 = 0 Reorder the terms: 49 + -30x + x2 = 0 Solving 49 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -30x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + -30x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -30x + x2 = 0 + -49 -30x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 -30x + x2 = -49 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -49 + 225 Reorder the terms: 225 + -30x + x2 = -49 + 225 Combine like terms: -49 + 225 = 176 225 + -30x + x2 = 176 Factor a perfect square on the left side: (x + -15)(x + -15) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (x + -15) equal to 13.266499161 and -13.266499161.Subproblem 1
x + -15 = 13.266499161 Simplifying x + -15 = 13.266499161 Reorder the terms: -15 + x = 13.266499161 Solving -15 + x = 13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 13.266499161 + 15 Combine like terms: -15 + 15 = 0 0 + x = 13.266499161 + 15 x = 13.266499161 + 15 Combine like terms: 13.266499161 + 15 = 28.266499161 x = 28.266499161 Simplifying x = 28.266499161Subproblem 2
x + -15 = -13.266499161 Simplifying x + -15 = -13.266499161 Reorder the terms: -15 + x = -13.266499161 Solving -15 + x = -13.266499161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -13.266499161 + 15 Combine like terms: -15 + 15 = 0 0 + x = -13.266499161 + 15 x = -13.266499161 + 15 Combine like terms: -13.266499161 + 15 = 1.733500839 x = 1.733500839 Simplifying x = 1.733500839Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.266499161, 1.733500839}
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