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Simplifying 6x(x + -2) = 36 + -10x Reorder the terms: 6x(-2 + x) = 36 + -10x (-2 * 6x + x * 6x) = 36 + -10x (-12x + 6x2) = 36 + -10x Solving -12x + 6x2 = 36 + -10x Solving for variable 'x'. Reorder the terms: -36 + -12x + 10x + 6x2 = 36 + -10x + -36 + 10x Combine like terms: -12x + 10x = -2x -36 + -2x + 6x2 = 36 + -10x + -36 + 10x Reorder the terms: -36 + -2x + 6x2 = 36 + -36 + -10x + 10x Combine like terms: 36 + -36 = 0 -36 + -2x + 6x2 = 0 + -10x + 10x -36 + -2x + 6x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -36 + -2x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -1x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying -18 + -1x + 3x2 = 0 Solving -18 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.3333333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -0.3333333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.3333333333x + x2 = 0 + 6 -0.3333333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.3333333333x + x2 = 6 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 = 6 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 6 + 0.02777777779 Combine like terms: 6 + 0.02777777779 = 6.02777777779 0.02777777779 + -0.3333333333x + x2 = 6.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 6.02777777779 Calculate the square root of the right side: 2.45515331 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 2.45515331 and -2.45515331.Subproblem 1
x + -0.1666666667 = 2.45515331 Simplifying x + -0.1666666667 = 2.45515331 Reorder the terms: -0.1666666667 + x = 2.45515331 Solving -0.1666666667 + x = 2.45515331 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 = 2.45515331 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 2.45515331 + 0.1666666667 x = 2.45515331 + 0.1666666667 Combine like terms: 2.45515331 + 0.1666666667 = 2.6218199767 x = 2.6218199767 Simplifying x = 2.6218199767Subproblem 2
x + -0.1666666667 = -2.45515331 Simplifying x + -0.1666666667 = -2.45515331 Reorder the terms: -0.1666666667 + x = -2.45515331 Solving -0.1666666667 + x = -2.45515331 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 = -2.45515331 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -2.45515331 + 0.1666666667 x = -2.45515331 + 0.1666666667 Combine like terms: -2.45515331 + 0.1666666667 = -2.2884866433 x = -2.2884866433 Simplifying x = -2.2884866433Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6218199767, -2.2884866433}Solution
x = {2.6218199767, -2.2884866433}
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