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Simplifying -8X2 + 48X = 4 Reorder the terms: 48X + -8X2 = 4 Solving 48X + -8X2 = 4 Solving for variable 'X'. Reorder the terms: -4 + 48X + -8X2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 48X + -8X2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + 12X + -2X2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + 12X + -2X2)' equal to zero and attempt to solve: Simplifying -1 + 12X + -2X2 = 0 Solving -1 + 12X + -2X2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -6X + X2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -6X + -0.5 + X2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -6X + X2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -6X + X2 = 0 + -0.5 -6X + X2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -6X + X2 = -0.5 The X term is -6X. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6X + 9 + X2 = -0.5 + 9 Reorder the terms: 9 + -6X + X2 = -0.5 + 9 Combine like terms: -0.5 + 9 = 8.5 9 + -6X + X2 = 8.5 Factor a perfect square on the left side: (X + -3)(X + -3) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (X + -3) equal to 2.915475947 and -2.915475947.Subproblem 1
X + -3 = 2.915475947 Simplifying X + -3 = 2.915475947 Reorder the terms: -3 + X = 2.915475947 Solving -3 + X = 2.915475947 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = 2.915475947 + 3 Combine like terms: -3 + 3 = 0 0 + X = 2.915475947 + 3 X = 2.915475947 + 3 Combine like terms: 2.915475947 + 3 = 5.915475947 X = 5.915475947 Simplifying X = 5.915475947Subproblem 2
X + -3 = -2.915475947 Simplifying X + -3 = -2.915475947 Reorder the terms: -3 + X = -2.915475947 Solving -3 + X = -2.915475947 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = -2.915475947 + 3 Combine like terms: -3 + 3 = 0 0 + X = -2.915475947 + 3 X = -2.915475947 + 3 Combine like terms: -2.915475947 + 3 = 0.084524053 X = 0.084524053 Simplifying X = 0.084524053Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.915475947, 0.084524053}Solution
X = {5.915475947, 0.084524053}
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