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Simplifying 5X2 = 32X + 12 Reorder the terms: 5X2 = 12 + 32X Solving 5X2 = 12 + 32X Solving for variable 'X'. Reorder the terms: -12 + -32X + 5X2 = 12 + 32X + -12 + -32X Reorder the terms: -12 + -32X + 5X2 = 12 + -12 + 32X + -32X Combine like terms: 12 + -12 = 0 -12 + -32X + 5X2 = 0 + 32X + -32X -12 + -32X + 5X2 = 32X + -32X Combine like terms: 32X + -32X = 0 -12 + -32X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -6.4X + X2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -6.4X + 2.4 + X2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -6.4X + X2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -6.4X + X2 = 0 + 2.4 -6.4X + X2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -6.4X + X2 = 2.4 The X term is -6.4X. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4X + 10.24 + X2 = 2.4 + 10.24 Reorder the terms: 10.24 + -6.4X + X2 = 2.4 + 10.24 Combine like terms: 2.4 + 10.24 = 12.64 10.24 + -6.4X + X2 = 12.64 Factor a perfect square on the left side: (X + -3.2)(X + -3.2) = 12.64 Calculate the square root of the right side: 3.555277767 Break this problem into two subproblems by setting (X + -3.2) equal to 3.555277767 and -3.555277767.Subproblem 1
X + -3.2 = 3.555277767 Simplifying X + -3.2 = 3.555277767 Reorder the terms: -3.2 + X = 3.555277767 Solving -3.2 + X = 3.555277767 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + X = 3.555277767 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + X = 3.555277767 + 3.2 X = 3.555277767 + 3.2 Combine like terms: 3.555277767 + 3.2 = 6.755277767 X = 6.755277767 Simplifying X = 6.755277767Subproblem 2
X + -3.2 = -3.555277767 Simplifying X + -3.2 = -3.555277767 Reorder the terms: -3.2 + X = -3.555277767 Solving -3.2 + X = -3.555277767 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + X = -3.555277767 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + X = -3.555277767 + 3.2 X = -3.555277767 + 3.2 Combine like terms: -3.555277767 + 3.2 = -0.355277767 X = -0.355277767 Simplifying X = -0.355277767Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.755277767, -0.355277767}
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