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Simplifying 14x2 + 24x + 2 = 0 Reorder the terms: 2 + 24x + 14x2 = 0 Solving 2 + 24x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 12x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 12x + 7x2)' equal to zero and attempt to solve: Simplifying 1 + 12x + 7x2 = 0 Solving 1 + 12x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 1.714285714x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 1.714285714x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 1.714285714x + x2 = 0 + -0.1428571429 1.714285714x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 1.714285714x + x2 = -0.1428571429 The x term is 1.714285714x. Take half its coefficient (0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. 1.714285714x + 0.7346938773 + x2 = -0.1428571429 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = -0.1428571429 + 0.7346938773 Combine like terms: -0.1428571429 + 0.7346938773 = 0.5918367344 0.7346938773 + 1.714285714x + x2 = 0.5918367344 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 0.5918367344 Calculate the square root of the right side: 0.769309258 Break this problem into two subproblems by setting (x + 0.857142857) equal to 0.769309258 and -0.769309258.Subproblem 1
x + 0.857142857 = 0.769309258 Simplifying x + 0.857142857 = 0.769309258 Reorder the terms: 0.857142857 + x = 0.769309258 Solving 0.857142857 + x = 0.769309258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = 0.769309258 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 0.769309258 + -0.857142857 x = 0.769309258 + -0.857142857 Combine like terms: 0.769309258 + -0.857142857 = -0.087833599 x = -0.087833599 Simplifying x = -0.087833599Subproblem 2
x + 0.857142857 = -0.769309258 Simplifying x + 0.857142857 = -0.769309258 Reorder the terms: 0.857142857 + x = -0.769309258 Solving 0.857142857 + x = -0.769309258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = -0.769309258 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -0.769309258 + -0.857142857 x = -0.769309258 + -0.857142857 Combine like terms: -0.769309258 + -0.857142857 = -1.626452115 x = -1.626452115 Simplifying x = -1.626452115Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.087833599, -1.626452115}Solution
x = {-0.087833599, -1.626452115}
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