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Simplifying 0 = 12x2 + -84x + 104 Reorder the terms: 0 = 104 + -84x + 12x2 Solving 0 = 104 + -84x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -104 = -104 -104 + 84x + -12x2 = 104 + -84x + 12x2 + -104 + 84x + -12x2 Reorder the terms: -104 + 84x + -12x2 = 104 + -104 + -84x + 84x + 12x2 + -12x2 Combine like terms: 104 + -104 = 0 -104 + 84x + -12x2 = 0 + -84x + 84x + 12x2 + -12x2 -104 + 84x + -12x2 = -84x + 84x + 12x2 + -12x2 Combine like terms: -84x + 84x = 0 -104 + 84x + -12x2 = 0 + 12x2 + -12x2 -104 + 84x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -104 + 84x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-26 + 21x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-26 + 21x + -3x2)' equal to zero and attempt to solve: Simplifying -26 + 21x + -3x2 = 0 Solving -26 + 21x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 8.666666667 + -7x + x2 = 0 Move the constant term to the right: Add '-8.666666667' to each side of the equation. 8.666666667 + -7x + -8.666666667 + x2 = 0 + -8.666666667 Reorder the terms: 8.666666667 + -8.666666667 + -7x + x2 = 0 + -8.666666667 Combine like terms: 8.666666667 + -8.666666667 = 0.000000000 0.000000000 + -7x + x2 = 0 + -8.666666667 -7x + x2 = 0 + -8.666666667 Combine like terms: 0 + -8.666666667 = -8.666666667 -7x + x2 = -8.666666667 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -8.666666667 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -8.666666667 + 12.25 Combine like terms: -8.666666667 + 12.25 = 3.583333333 12.25 + -7x + x2 = 3.583333333 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (x + -3.5) equal to 1.892969449 and -1.892969449.Subproblem 1
x + -3.5 = 1.892969449 Simplifying x + -3.5 = 1.892969449 Reorder the terms: -3.5 + x = 1.892969449 Solving -3.5 + x = 1.892969449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.892969449 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.892969449 + 3.5 x = 1.892969449 + 3.5 Combine like terms: 1.892969449 + 3.5 = 5.392969449 x = 5.392969449 Simplifying x = 5.392969449Subproblem 2
x + -3.5 = -1.892969449 Simplifying x + -3.5 = -1.892969449 Reorder the terms: -3.5 + x = -1.892969449 Solving -3.5 + x = -1.892969449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.892969449 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.892969449 + 3.5 x = -1.892969449 + 3.5 Combine like terms: -1.892969449 + 3.5 = 1.607030551 x = 1.607030551 Simplifying x = 1.607030551Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.392969449, 1.607030551}Solution
x = {5.392969449, 1.607030551}
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