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Simplifying 14x2 = 86x + 12 Reorder the terms: 14x2 = 12 + 86x Solving 14x2 = 12 + 86x Solving for variable 'x'. Reorder the terms: -12 + -86x + 14x2 = 12 + 86x + -12 + -86x Reorder the terms: -12 + -86x + 14x2 = 12 + -12 + 86x + -86x Combine like terms: 12 + -12 = 0 -12 + -86x + 14x2 = 0 + 86x + -86x -12 + -86x + 14x2 = 86x + -86x Combine like terms: 86x + -86x = 0 -12 + -86x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -43x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -43x + 7x2)' equal to zero and attempt to solve: Simplifying -6 + -43x + 7x2 = 0 Solving -6 + -43x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + -6.142857143x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -6.142857143x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -6.142857143x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -6.142857143x + x2 = 0 + 0.8571428571 -6.142857143x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -6.142857143x + x2 = 0.8571428571 The x term is -6.142857143x. Take half its coefficient (-3.071428572). Square it (9.433673473) and add it to both sides. Add '9.433673473' to each side of the equation. -6.142857143x + 9.433673473 + x2 = 0.8571428571 + 9.433673473 Reorder the terms: 9.433673473 + -6.142857143x + x2 = 0.8571428571 + 9.433673473 Combine like terms: 0.8571428571 + 9.433673473 = 10.2908163301 9.433673473 + -6.142857143x + x2 = 10.2908163301 Factor a perfect square on the left side: (x + -3.071428572)(x + -3.071428572) = 10.2908163301 Calculate the square root of the right side: 3.207930225 Break this problem into two subproblems by setting (x + -3.071428572) equal to 3.207930225 and -3.207930225.Subproblem 1
x + -3.071428572 = 3.207930225 Simplifying x + -3.071428572 = 3.207930225 Reorder the terms: -3.071428572 + x = 3.207930225 Solving -3.071428572 + x = 3.207930225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.071428572' to each side of the equation. -3.071428572 + 3.071428572 + x = 3.207930225 + 3.071428572 Combine like terms: -3.071428572 + 3.071428572 = 0.000000000 0.000000000 + x = 3.207930225 + 3.071428572 x = 3.207930225 + 3.071428572 Combine like terms: 3.207930225 + 3.071428572 = 6.279358797 x = 6.279358797 Simplifying x = 6.279358797Subproblem 2
x + -3.071428572 = -3.207930225 Simplifying x + -3.071428572 = -3.207930225 Reorder the terms: -3.071428572 + x = -3.207930225 Solving -3.071428572 + x = -3.207930225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.071428572' to each side of the equation. -3.071428572 + 3.071428572 + x = -3.207930225 + 3.071428572 Combine like terms: -3.071428572 + 3.071428572 = 0.000000000 0.000000000 + x = -3.207930225 + 3.071428572 x = -3.207930225 + 3.071428572 Combine like terms: -3.207930225 + 3.071428572 = -0.136501653 x = -0.136501653 Simplifying x = -0.136501653Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.279358797, -0.136501653}Solution
x = {6.279358797, -0.136501653}
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