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Simplifying x2 + -30x + -176 = 0 Reorder the terms: -176 + -30x + x2 = 0 Solving -176 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '176' to each side of the equation. -176 + -30x + 176 + x2 = 0 + 176 Reorder the terms: -176 + 176 + -30x + x2 = 0 + 176 Combine like terms: -176 + 176 = 0 0 + -30x + x2 = 0 + 176 -30x + x2 = 0 + 176 Combine like terms: 0 + 176 = 176 -30x + x2 = 176 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 = 176 + 225 Reorder the terms: 225 + -30x + x2 = 176 + 225 Combine like terms: 176 + 225 = 401 225 + -30x + x2 = 401 Factor a perfect square on the left side: (x + -15)(x + -15) = 401 Calculate the square root of the right side: 20.024984395 Break this problem into two subproblems by setting (x + -15) equal to 20.024984395 and -20.024984395.Subproblem 1
x + -15 = 20.024984395 Simplifying x + -15 = 20.024984395 Reorder the terms: -15 + x = 20.024984395 Solving -15 + x = 20.024984395 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 = 20.024984395 + 15 Combine like terms: -15 + 15 = 0 0 + x = 20.024984395 + 15 x = 20.024984395 + 15 Combine like terms: 20.024984395 + 15 = 35.024984395 x = 35.024984395 Simplifying x = 35.024984395Subproblem 2
x + -15 = -20.024984395 Simplifying x + -15 = -20.024984395 Reorder the terms: -15 + x = -20.024984395 Solving -15 + x = -20.024984395 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 = -20.024984395 + 15 Combine like terms: -15 + 15 = 0 0 + x = -20.024984395 + 15 x = -20.024984395 + 15 Combine like terms: -20.024984395 + 15 = -5.024984395 x = -5.024984395 Simplifying x = -5.024984395Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.024984395, -5.024984395}
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