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Simplifying 14x2 + 12 + -6x = 30 + -4x2 + 8 Reorder the terms: 12 + -6x + 14x2 = 30 + -4x2 + 8 Reorder the terms: 12 + -6x + 14x2 = 30 + 8 + -4x2 Combine like terms: 30 + 8 = 38 12 + -6x + 14x2 = 38 + -4x2 Solving 12 + -6x + 14x2 = 38 + -4x2 Solving for variable 'x'. Reorder the terms: 12 + -38 + -6x + 14x2 + 4x2 = 38 + -4x2 + -38 + 4x2 Combine like terms: 12 + -38 = -26 -26 + -6x + 14x2 + 4x2 = 38 + -4x2 + -38 + 4x2 Combine like terms: 14x2 + 4x2 = 18x2 -26 + -6x + 18x2 = 38 + -4x2 + -38 + 4x2 Reorder the terms: -26 + -6x + 18x2 = 38 + -38 + -4x2 + 4x2 Combine like terms: 38 + -38 = 0 -26 + -6x + 18x2 = 0 + -4x2 + 4x2 -26 + -6x + 18x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -26 + -6x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -3x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -3x + 9x2)' equal to zero and attempt to solve: Simplifying -13 + -3x + 9x2 = 0 Solving -13 + -3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.444444444 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '1.444444444' to each side of the equation. -1.444444444 + -0.3333333333x + 1.444444444 + x2 = 0 + 1.444444444 Reorder the terms: -1.444444444 + 1.444444444 + -0.3333333333x + x2 = 0 + 1.444444444 Combine like terms: -1.444444444 + 1.444444444 = 0.000000000 0.000000000 + -0.3333333333x + x2 = 0 + 1.444444444 -0.3333333333x + x2 = 0 + 1.444444444 Combine like terms: 0 + 1.444444444 = 1.444444444 -0.3333333333x + x2 = 1.444444444 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 1.444444444 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 1.444444444 + 0.02777777779 Combine like terms: 1.444444444 + 0.02777777779 = 1.47222222179 0.02777777779 + -0.3333333333x + x2 = 1.47222222179 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 1.47222222179 Calculate the square root of the right side: 1.213351648 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 1.213351648 and -1.213351648.Subproblem 1
x + -0.1666666667 = 1.213351648 Simplifying x + -0.1666666667 = 1.213351648 Reorder the terms: -0.1666666667 + x = 1.213351648 Solving -0.1666666667 + x = 1.213351648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 1.213351648 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 1.213351648 + 0.1666666667 x = 1.213351648 + 0.1666666667 Combine like terms: 1.213351648 + 0.1666666667 = 1.3800183147 x = 1.3800183147 Simplifying x = 1.3800183147Subproblem 2
x + -0.1666666667 = -1.213351648 Simplifying x + -0.1666666667 = -1.213351648 Reorder the terms: -0.1666666667 + x = -1.213351648 Solving -0.1666666667 + x = -1.213351648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -1.213351648 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -1.213351648 + 0.1666666667 x = -1.213351648 + 0.1666666667 Combine like terms: -1.213351648 + 0.1666666667 = -1.0466849813 x = -1.0466849813 Simplifying x = -1.0466849813Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3800183147, -1.0466849813}Solution
x = {1.3800183147, -1.0466849813}
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