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Simplifying (x + -15)(x + -15) = 28 Reorder the terms: (-15 + x)(x + -15) = 28 Reorder the terms: (-15 + x)(-15 + x) = 28 Multiply (-15 + x) * (-15 + x) (-15(-15 + x) + x(-15 + x)) = 28 ((-15 * -15 + x * -15) + x(-15 + x)) = 28 ((225 + -15x) + x(-15 + x)) = 28 (225 + -15x + (-15 * x + x * x)) = 28 (225 + -15x + (-15x + x2)) = 28 Combine like terms: -15x + -15x = -30x (225 + -30x + x2) = 28 Solving 225 + -30x + x2 = 28 Solving for variable 'x'. Reorder the terms: 225 + -28 + -30x + x2 = 28 + -28 Combine like terms: 225 + -28 = 197 197 + -30x + x2 = 28 + -28 Combine like terms: 28 + -28 = 0 197 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-197' to each side of the equation. 197 + -30x + -197 + x2 = 0 + -197 Reorder the terms: 197 + -197 + -30x + x2 = 0 + -197 Combine like terms: 197 + -197 = 0 0 + -30x + x2 = 0 + -197 -30x + x2 = 0 + -197 Combine like terms: 0 + -197 = -197 -30x + x2 = -197 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 = -197 + 225 Reorder the terms: 225 + -30x + x2 = -197 + 225 Combine like terms: -197 + 225 = 28 225 + -30x + x2 = 28 Factor a perfect square on the left side: (x + -15)(x + -15) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -15) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -15 = 5.291502622 Simplifying x + -15 = 5.291502622 Reorder the terms: -15 + x = 5.291502622 Solving -15 + x = 5.291502622 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 = 5.291502622 + 15 Combine like terms: -15 + 15 = 0 0 + x = 5.291502622 + 15 x = 5.291502622 + 15 Combine like terms: 5.291502622 + 15 = 20.291502622 x = 20.291502622 Simplifying x = 20.291502622Subproblem 2
x + -15 = -5.291502622 Simplifying x + -15 = -5.291502622 Reorder the terms: -15 + x = -5.291502622 Solving -15 + x = -5.291502622 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 = -5.291502622 + 15 Combine like terms: -15 + 15 = 0 0 + x = -5.291502622 + 15 x = -5.291502622 + 15 Combine like terms: -5.291502622 + 15 = 9.708497378 x = 9.708497378 Simplifying x = 9.708497378Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.291502622, 9.708497378}
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