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Simplifying -12X2 + 72X + -78 = 0 Reorder the terms: -78 + 72X + -12X2 = 0 Solving -78 + 72X + -12X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '6'. 6(-13 + 12X + -2X2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-13 + 12X + -2X2)' equal to zero and attempt to solve: Simplifying -13 + 12X + -2X2 = 0 Solving -13 + 12X + -2X2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 6.5 + -6X + X2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -6X + -6.5 + X2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -6X + X2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -6X + X2 = 0 + -6.5 -6X + X2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -6X + X2 = -6.5 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 = -6.5 + 9 Reorder the terms: 9 + -6X + X2 = -6.5 + 9 Combine like terms: -6.5 + 9 = 2.5 9 + -6X + X2 = 2.5 Factor a perfect square on the left side: (X + -3)(X + -3) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (X + -3) equal to 1.58113883 and -1.58113883.Subproblem 1
X + -3 = 1.58113883 Simplifying X + -3 = 1.58113883 Reorder the terms: -3 + X = 1.58113883 Solving -3 + X = 1.58113883 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 = 1.58113883 + 3 Combine like terms: -3 + 3 = 0 0 + X = 1.58113883 + 3 X = 1.58113883 + 3 Combine like terms: 1.58113883 + 3 = 4.58113883 X = 4.58113883 Simplifying X = 4.58113883Subproblem 2
X + -3 = -1.58113883 Simplifying X + -3 = -1.58113883 Reorder the terms: -3 + X = -1.58113883 Solving -3 + X = -1.58113883 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 = -1.58113883 + 3 Combine like terms: -3 + 3 = 0 0 + X = -1.58113883 + 3 X = -1.58113883 + 3 Combine like terms: -1.58113883 + 3 = 1.41886117 X = 1.41886117 Simplifying X = 1.41886117Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.58113883, 1.41886117}Solution
X = {4.58113883, 1.41886117}
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