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Simplifying 6x2 + -29x + -42 = 9x Reorder the terms: -42 + -29x + 6x2 = 9x Solving -42 + -29x + 6x2 = 9x Solving for variable 'x'. Reorder the terms: -42 + -29x + -9x + 6x2 = 9x + -9x Combine like terms: -29x + -9x = -38x -42 + -38x + 6x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -42 + -38x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -19x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -19x + 3x2)' equal to zero and attempt to solve: Simplifying -21 + -19x + 3x2 = 0 Solving -21 + -19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7 + -6.333333333x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -6.333333333x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -6.333333333x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -6.333333333x + x2 = 0 + 7 -6.333333333x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -6.333333333x + x2 = 7 The x term is -6.333333333x. Take half its coefficient (-3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. -6.333333333x + 10.02777778 + x2 = 7 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333x + x2 = 7 + 10.02777778 Combine like terms: 7 + 10.02777778 = 17.02777778 10.02777778 + -6.333333333x + x2 = 17.02777778 Factor a perfect square on the left side: (x + -3.166666667)(x + -3.166666667) = 17.02777778 Calculate the square root of the right side: 4.126472801 Break this problem into two subproblems by setting (x + -3.166666667) equal to 4.126472801 and -4.126472801.Subproblem 1
x + -3.166666667 = 4.126472801 Simplifying x + -3.166666667 = 4.126472801 Reorder the terms: -3.166666667 + x = 4.126472801 Solving -3.166666667 + x = 4.126472801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = 4.126472801 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = 4.126472801 + 3.166666667 x = 4.126472801 + 3.166666667 Combine like terms: 4.126472801 + 3.166666667 = 7.293139468 x = 7.293139468 Simplifying x = 7.293139468Subproblem 2
x + -3.166666667 = -4.126472801 Simplifying x + -3.166666667 = -4.126472801 Reorder the terms: -3.166666667 + x = -4.126472801 Solving -3.166666667 + x = -4.126472801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.166666667' to each side of the equation. -3.166666667 + 3.166666667 + x = -4.126472801 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + x = -4.126472801 + 3.166666667 x = -4.126472801 + 3.166666667 Combine like terms: -4.126472801 + 3.166666667 = -0.959806134 x = -0.959806134 Simplifying x = -0.959806134Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.293139468, -0.959806134}Solution
x = {7.293139468, -0.959806134}
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