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Simplifying 6x2 + -12x + -14 = 14x Reorder the terms: -14 + -12x + 6x2 = 14x Solving -14 + -12x + 6x2 = 14x Solving for variable 'x'. Reorder the terms: -14 + -12x + -14x + 6x2 = 14x + -14x Combine like terms: -12x + -14x = -26x -14 + -26x + 6x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -14 + -26x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -13x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -13x + 3x2)' equal to zero and attempt to solve: Simplifying -7 + -13x + 3x2 = 0 Solving -7 + -13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + -4.333333333x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -4.333333333x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -4.333333333x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -4.333333333x + x2 = 0 + 2.333333333 -4.333333333x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -4.333333333x + x2 = 2.333333333 The x term is -4.333333333x. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333x + 4.694444446 + x2 = 2.333333333 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333x + x2 = 2.333333333 + 4.694444446 Combine like terms: 2.333333333 + 4.694444446 = 7.027777779 4.694444446 + -4.333333333x + x2 = 7.027777779 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 7.027777779 Calculate the square root of the right side: 2.65099562 Break this problem into two subproblems by setting (x + -2.166666667) equal to 2.65099562 and -2.65099562.Subproblem 1
x + -2.166666667 = 2.65099562 Simplifying x + -2.166666667 = 2.65099562 Reorder the terms: -2.166666667 + x = 2.65099562 Solving -2.166666667 + x = 2.65099562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = 2.65099562 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 2.65099562 + 2.166666667 x = 2.65099562 + 2.166666667 Combine like terms: 2.65099562 + 2.166666667 = 4.817662287 x = 4.817662287 Simplifying x = 4.817662287Subproblem 2
x + -2.166666667 = -2.65099562 Simplifying x + -2.166666667 = -2.65099562 Reorder the terms: -2.166666667 + x = -2.65099562 Solving -2.166666667 + x = -2.65099562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = -2.65099562 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -2.65099562 + 2.166666667 x = -2.65099562 + 2.166666667 Combine like terms: -2.65099562 + 2.166666667 = -0.484328953 x = -0.484328953 Simplifying x = -0.484328953Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.817662287, -0.484328953}Solution
x = {4.817662287, -0.484328953}
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