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Simplifying 14x2 + 84x + 12 = 0 Reorder the terms: 12 + 84x + 14x2 = 0 Solving 12 + 84x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 42x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 42x + 7x2)' equal to zero and attempt to solve: Simplifying 6 + 42x + 7x2 = 0 Solving 6 + 42x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 6x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 6x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 6x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 6x + x2 = 0 + -0.8571428571 6x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 6x + x2 = -0.8571428571 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 = -0.8571428571 + 9 Reorder the terms: 9 + 6x + x2 = -0.8571428571 + 9 Combine like terms: -0.8571428571 + 9 = 8.1428571429 9 + 6x + x2 = 8.1428571429 Factor a perfect square on the left side: (x + 3)(x + 3) = 8.1428571429 Calculate the square root of the right side: 2.853569194 Break this problem into two subproblems by setting (x + 3) equal to 2.853569194 and -2.853569194.Subproblem 1
x + 3 = 2.853569194 Simplifying x + 3 = 2.853569194 Reorder the terms: 3 + x = 2.853569194 Solving 3 + x = 2.853569194 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 = 2.853569194 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.853569194 + -3 x = 2.853569194 + -3 Combine like terms: 2.853569194 + -3 = -0.146430806 x = -0.146430806 Simplifying x = -0.146430806Subproblem 2
x + 3 = -2.853569194 Simplifying x + 3 = -2.853569194 Reorder the terms: 3 + x = -2.853569194 Solving 3 + x = -2.853569194 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 = -2.853569194 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.853569194 + -3 x = -2.853569194 + -3 Combine like terms: -2.853569194 + -3 = -5.853569194 x = -5.853569194 Simplifying x = -5.853569194Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.146430806, -5.853569194}Solution
x = {-0.146430806, -5.853569194}
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