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Simplifying 5X2 + -32X + 36 = 0 Reorder the terms: 36 + -32X + 5X2 = 0 Solving 36 + -32X + 5X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.2 + -6.4X + X2 = 0 Move the constant term to the right: Add '-7.2' to each side of the equation. 7.2 + -6.4X + -7.2 + X2 = 0 + -7.2 Reorder the terms: 7.2 + -7.2 + -6.4X + X2 = 0 + -7.2 Combine like terms: 7.2 + -7.2 = 0.0 0.0 + -6.4X + X2 = 0 + -7.2 -6.4X + X2 = 0 + -7.2 Combine like terms: 0 + -7.2 = -7.2 -6.4X + X2 = -7.2 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 = -7.2 + 10.24 Reorder the terms: 10.24 + -6.4X + X2 = -7.2 + 10.24 Combine like terms: -7.2 + 10.24 = 3.04 10.24 + -6.4X + X2 = 3.04 Factor a perfect square on the left side: (X + -3.2)(X + -3.2) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (X + -3.2) equal to 1.743559577 and -1.743559577.Subproblem 1
X + -3.2 = 1.743559577 Simplifying X + -3.2 = 1.743559577 Reorder the terms: -3.2 + X = 1.743559577 Solving -3.2 + X = 1.743559577 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 = 1.743559577 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + X = 1.743559577 + 3.2 X = 1.743559577 + 3.2 Combine like terms: 1.743559577 + 3.2 = 4.943559577 X = 4.943559577 Simplifying X = 4.943559577Subproblem 2
X + -3.2 = -1.743559577 Simplifying X + -3.2 = -1.743559577 Reorder the terms: -3.2 + X = -1.743559577 Solving -3.2 + X = -1.743559577 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 = -1.743559577 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + X = -1.743559577 + 3.2 X = -1.743559577 + 3.2 Combine like terms: -1.743559577 + 3.2 = 1.456440423 X = 1.456440423 Simplifying X = 1.456440423Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.943559577, 1.456440423}
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