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Simplifying 2X2 + -15X + -16 = 0 Reorder the terms: -16 + -15X + 2X2 = 0 Solving -16 + -15X + 2X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + -7.5X + X2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -7.5X + 8 + X2 = 0 + 8 Reorder the terms: -8 + 8 + -7.5X + X2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7.5X + X2 = 0 + 8 -7.5X + X2 = 0 + 8 Combine like terms: 0 + 8 = 8 -7.5X + X2 = 8 The X term is -7.5X. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5X + 14.0625 + X2 = 8 + 14.0625 Reorder the terms: 14.0625 + -7.5X + X2 = 8 + 14.0625 Combine like terms: 8 + 14.0625 = 22.0625 14.0625 + -7.5X + X2 = 22.0625 Factor a perfect square on the left side: (X + -3.75)(X + -3.75) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (X + -3.75) equal to 4.697073557 and -4.697073557.Subproblem 1
X + -3.75 = 4.697073557 Simplifying X + -3.75 = 4.697073557 Reorder the terms: -3.75 + X = 4.697073557 Solving -3.75 + X = 4.697073557 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + X = 4.697073557 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + X = 4.697073557 + 3.75 X = 4.697073557 + 3.75 Combine like terms: 4.697073557 + 3.75 = 8.447073557 X = 8.447073557 Simplifying X = 8.447073557Subproblem 2
X + -3.75 = -4.697073557 Simplifying X + -3.75 = -4.697073557 Reorder the terms: -3.75 + X = -4.697073557 Solving -3.75 + X = -4.697073557 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + X = -4.697073557 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + X = -4.697073557 + 3.75 X = -4.697073557 + 3.75 Combine like terms: -4.697073557 + 3.75 = -0.947073557 X = -0.947073557 Simplifying X = -0.947073557Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.447073557, -0.947073557}
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