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Simplifying 72x + -12x2 + 170 = 0 Reorder the terms: 170 + 72x + -12x2 = 0 Solving 170 + 72x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(85 + 36x + -6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(85 + 36x + -6x2)' equal to zero and attempt to solve: Simplifying 85 + 36x + -6x2 = 0 Solving 85 + 36x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -14.16666667 + -6x + x2 = 0 Move the constant term to the right: Add '14.16666667' to each side of the equation. -14.16666667 + -6x + 14.16666667 + x2 = 0 + 14.16666667 Reorder the terms: -14.16666667 + 14.16666667 + -6x + x2 = 0 + 14.16666667 Combine like terms: -14.16666667 + 14.16666667 = 0.00000000 0.00000000 + -6x + x2 = 0 + 14.16666667 -6x + x2 = 0 + 14.16666667 Combine like terms: 0 + 14.16666667 = 14.16666667 -6x + x2 = 14.16666667 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 = 14.16666667 + 9 Reorder the terms: 9 + -6x + x2 = 14.16666667 + 9 Combine like terms: 14.16666667 + 9 = 23.16666667 9 + -6x + x2 = 23.16666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 23.16666667 Calculate the square root of the right side: 4.81317636 Break this problem into two subproblems by setting (x + -3) equal to 4.81317636 and -4.81317636.Subproblem 1
x + -3 = 4.81317636 Simplifying x + -3 = 4.81317636 Reorder the terms: -3 + x = 4.81317636 Solving -3 + x = 4.81317636 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 = 4.81317636 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.81317636 + 3 x = 4.81317636 + 3 Combine like terms: 4.81317636 + 3 = 7.81317636 x = 7.81317636 Simplifying x = 7.81317636Subproblem 2
x + -3 = -4.81317636 Simplifying x + -3 = -4.81317636 Reorder the terms: -3 + x = -4.81317636 Solving -3 + x = -4.81317636 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 = -4.81317636 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.81317636 + 3 x = -4.81317636 + 3 Combine like terms: -4.81317636 + 3 = -1.81317636 x = -1.81317636 Simplifying x = -1.81317636Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.81317636, -1.81317636}Solution
x = {7.81317636, -1.81317636}
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