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Simplifying 0 = 2X2 + -48X + 40 Reorder the terms: 0 = 40 + -48X + 2X2 Solving 0 = 40 + -48X + 2X2 Solving for variable 'X'. Combine like terms: 0 + -40 = -40 -40 + 48X + -2X2 = 40 + -48X + 2X2 + -40 + 48X + -2X2 Reorder the terms: -40 + 48X + -2X2 = 40 + -40 + -48X + 48X + 2X2 + -2X2 Combine like terms: 40 + -40 = 0 -40 + 48X + -2X2 = 0 + -48X + 48X + 2X2 + -2X2 -40 + 48X + -2X2 = -48X + 48X + 2X2 + -2X2 Combine like terms: -48X + 48X = 0 -40 + 48X + -2X2 = 0 + 2X2 + -2X2 -40 + 48X + -2X2 = 2X2 + -2X2 Combine like terms: 2X2 + -2X2 = 0 -40 + 48X + -2X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 24X + -1X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + 24X + -1X2)' equal to zero and attempt to solve: Simplifying -20 + 24X + -1X2 = 0 Solving -20 + 24X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -24X + X2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -24X + -20 + X2 = 0 + -20 Reorder the terms: 20 + -20 + -24X + X2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -24X + X2 = 0 + -20 -24X + X2 = 0 + -20 Combine like terms: 0 + -20 = -20 -24X + X2 = -20 The X term is -24X. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24X + 144 + X2 = -20 + 144 Reorder the terms: 144 + -24X + X2 = -20 + 144 Combine like terms: -20 + 144 = 124 144 + -24X + X2 = 124 Factor a perfect square on the left side: (X + -12)(X + -12) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (X + -12) equal to 11.135528726 and -11.135528726.Subproblem 1
X + -12 = 11.135528726 Simplifying X + -12 = 11.135528726 Reorder the terms: -12 + X = 11.135528726 Solving -12 + X = 11.135528726 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + X = 11.135528726 + 12 Combine like terms: -12 + 12 = 0 0 + X = 11.135528726 + 12 X = 11.135528726 + 12 Combine like terms: 11.135528726 + 12 = 23.135528726 X = 23.135528726 Simplifying X = 23.135528726Subproblem 2
X + -12 = -11.135528726 Simplifying X + -12 = -11.135528726 Reorder the terms: -12 + X = -11.135528726 Solving -12 + X = -11.135528726 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + X = -11.135528726 + 12 Combine like terms: -12 + 12 = 0 0 + X = -11.135528726 + 12 X = -11.135528726 + 12 Combine like terms: -11.135528726 + 12 = 0.864471274 X = 0.864471274 Simplifying X = 0.864471274Solution
The solution to the problem is based on the solutions from the subproblems. X = {23.135528726, 0.864471274}Solution
X = {23.135528726, 0.864471274}
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