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Simplifying 14x2 + -24x + -12 = 0 Reorder the terms: -12 + -24x + 14x2 = 0 Solving -12 + -24x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -12x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -12x + 7x2)' equal to zero and attempt to solve: Simplifying -6 + -12x + 7x2 = 0 Solving -6 + -12x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + -1.714285714x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + -1.714285714x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + -1.714285714x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + -1.714285714x + x2 = 0 + 0.8571428571 -1.714285714x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 -1.714285714x + x2 = 0.8571428571 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 = 0.8571428571 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714x + x2 = 0.8571428571 + 0.7346938773 Combine like terms: 0.8571428571 + 0.7346938773 = 1.5918367344 0.7346938773 + -1.714285714x + x2 = 1.5918367344 Factor a perfect square on the left side: (x + -0.857142857)(x + -0.857142857) = 1.5918367344 Calculate the square root of the right side: 1.261680124 Break this problem into two subproblems by setting (x + -0.857142857) equal to 1.261680124 and -1.261680124.Subproblem 1
x + -0.857142857 = 1.261680124 Simplifying x + -0.857142857 = 1.261680124 Reorder the terms: -0.857142857 + x = 1.261680124 Solving -0.857142857 + x = 1.261680124 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 = 1.261680124 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = 1.261680124 + 0.857142857 x = 1.261680124 + 0.857142857 Combine like terms: 1.261680124 + 0.857142857 = 2.118822981 x = 2.118822981 Simplifying x = 2.118822981Subproblem 2
x + -0.857142857 = -1.261680124 Simplifying x + -0.857142857 = -1.261680124 Reorder the terms: -0.857142857 + x = -1.261680124 Solving -0.857142857 + x = -1.261680124 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 = -1.261680124 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + x = -1.261680124 + 0.857142857 x = -1.261680124 + 0.857142857 Combine like terms: -1.261680124 + 0.857142857 = -0.404537267 x = -0.404537267 Simplifying x = -0.404537267Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.118822981, -0.404537267}Solution
x = {2.118822981, -0.404537267}
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