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Simplifying 12x2 + 4x + -6 = 0 Reorder the terms: -6 + 4x + 12x2 = 0 Solving -6 + 4x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 2x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 2x + 6x2)' equal to zero and attempt to solve: Simplifying -3 + 2x + 6x2 = 0 Solving -3 + 2x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.3333333333x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.3333333333x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.3333333333x + x2 = 0 + 0.5 0.3333333333x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.3333333333x + x2 = 0.5 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 = 0.5 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.5 + 0.02777777779 Combine like terms: 0.5 + 0.02777777779 = 0.52777777779 0.02777777779 + 0.3333333333x + x2 = 0.52777777779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.52777777779 Calculate the square root of the right side: 0.726483157 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.726483157 and -0.726483157.Subproblem 1
x + 0.1666666667 = 0.726483157 Simplifying x + 0.1666666667 = 0.726483157 Reorder the terms: 0.1666666667 + x = 0.726483157 Solving 0.1666666667 + x = 0.726483157 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 = 0.726483157 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.726483157 + -0.1666666667 x = 0.726483157 + -0.1666666667 Combine like terms: 0.726483157 + -0.1666666667 = 0.5598164903 x = 0.5598164903 Simplifying x = 0.5598164903Subproblem 2
x + 0.1666666667 = -0.726483157 Simplifying x + 0.1666666667 = -0.726483157 Reorder the terms: 0.1666666667 + x = -0.726483157 Solving 0.1666666667 + x = -0.726483157 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 = -0.726483157 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.726483157 + -0.1666666667 x = -0.726483157 + -0.1666666667 Combine like terms: -0.726483157 + -0.1666666667 = -0.8931498237 x = -0.8931498237 Simplifying x = -0.8931498237Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5598164903, -0.8931498237}Solution
x = {0.5598164903, -0.8931498237}
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