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Simplifying 16X2 + 73X + 60 = 0 Reorder the terms: 60 + 73X + 16X2 = 0 Solving 60 + 73X + 16X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.75 + 4.5625X + X2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 4.5625X + -3.75 + X2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 4.5625X + X2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 4.5625X + X2 = 0 + -3.75 4.5625X + X2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 4.5625X + X2 = -3.75 The X term is 4.5625X. Take half its coefficient (2.28125). Square it (5.204101563) and add it to both sides. Add '5.204101563' to each side of the equation. 4.5625X + 5.204101563 + X2 = -3.75 + 5.204101563 Reorder the terms: 5.204101563 + 4.5625X + X2 = -3.75 + 5.204101563 Combine like terms: -3.75 + 5.204101563 = 1.454101563 5.204101563 + 4.5625X + X2 = 1.454101563 Factor a perfect square on the left side: (X + 2.28125)(X + 2.28125) = 1.454101563 Calculate the square root of the right side: 1.205861337 Break this problem into two subproblems by setting (X + 2.28125) equal to 1.205861337 and -1.205861337.Subproblem 1
X + 2.28125 = 1.205861337 Simplifying X + 2.28125 = 1.205861337 Reorder the terms: 2.28125 + X = 1.205861337 Solving 2.28125 + X = 1.205861337 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.28125' to each side of the equation. 2.28125 + -2.28125 + X = 1.205861337 + -2.28125 Combine like terms: 2.28125 + -2.28125 = 0.00000 0.00000 + X = 1.205861337 + -2.28125 X = 1.205861337 + -2.28125 Combine like terms: 1.205861337 + -2.28125 = -1.075388663 X = -1.075388663 Simplifying X = -1.075388663Subproblem 2
X + 2.28125 = -1.205861337 Simplifying X + 2.28125 = -1.205861337 Reorder the terms: 2.28125 + X = -1.205861337 Solving 2.28125 + X = -1.205861337 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.28125' to each side of the equation. 2.28125 + -2.28125 + X = -1.205861337 + -2.28125 Combine like terms: 2.28125 + -2.28125 = 0.00000 0.00000 + X = -1.205861337 + -2.28125 X = -1.205861337 + -2.28125 Combine like terms: -1.205861337 + -2.28125 = -3.487111337 X = -3.487111337 Simplifying X = -3.487111337Solution
The solution to the problem is based on the solutions from the subproblems. X = {-1.075388663, -3.487111337}
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