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Simplifying 6x2 + -66x + 68 = 0 Reorder the terms: 68 + -66x + 6x2 = 0 Solving 68 + -66x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(34 + -33x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(34 + -33x + 3x2)' equal to zero and attempt to solve: Simplifying 34 + -33x + 3x2 = 0 Solving 34 + -33x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 11.33333333 + -11x + x2 = 0 Move the constant term to the right: Add '-11.33333333' to each side of the equation. 11.33333333 + -11x + -11.33333333 + x2 = 0 + -11.33333333 Reorder the terms: 11.33333333 + -11.33333333 + -11x + x2 = 0 + -11.33333333 Combine like terms: 11.33333333 + -11.33333333 = 0.00000000 0.00000000 + -11x + x2 = 0 + -11.33333333 -11x + x2 = 0 + -11.33333333 Combine like terms: 0 + -11.33333333 = -11.33333333 -11x + x2 = -11.33333333 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -11.33333333 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -11.33333333 + 30.25 Combine like terms: -11.33333333 + 30.25 = 18.91666667 30.25 + -11x + x2 = 18.91666667 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 18.91666667 Calculate the square root of the right side: 4.349329451 Break this problem into two subproblems by setting (x + -5.5) equal to 4.349329451 and -4.349329451.Subproblem 1
x + -5.5 = 4.349329451 Simplifying x + -5.5 = 4.349329451 Reorder the terms: -5.5 + x = 4.349329451 Solving -5.5 + x = 4.349329451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 4.349329451 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 4.349329451 + 5.5 x = 4.349329451 + 5.5 Combine like terms: 4.349329451 + 5.5 = 9.849329451 x = 9.849329451 Simplifying x = 9.849329451Subproblem 2
x + -5.5 = -4.349329451 Simplifying x + -5.5 = -4.349329451 Reorder the terms: -5.5 + x = -4.349329451 Solving -5.5 + x = -4.349329451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -4.349329451 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -4.349329451 + 5.5 x = -4.349329451 + 5.5 Combine like terms: -4.349329451 + 5.5 = 1.150670549 x = 1.150670549 Simplifying x = 1.150670549Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.849329451, 1.150670549}Solution
x = {9.849329451, 1.150670549}
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