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Simplifying 12x2 + 46x + -42 = 0 Reorder the terms: -42 + 46x + 12x2 = 0 Solving -42 + 46x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 23x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + 23x + 6x2)' equal to zero and attempt to solve: Simplifying -21 + 23x + 6x2 = 0 Solving -21 + 23x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.5 + 3.833333333x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 3.833333333x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 3.833333333x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 3.833333333x + x2 = 0 + 3.5 3.833333333x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 3.833333333x + x2 = 3.5 The x term is 3.833333333x. Take half its coefficient (1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. 3.833333333x + 3.673611112 + x2 = 3.5 + 3.673611112 Reorder the terms: 3.673611112 + 3.833333333x + x2 = 3.5 + 3.673611112 Combine like terms: 3.5 + 3.673611112 = 7.173611112 3.673611112 + 3.833333333x + x2 = 7.173611112 Factor a perfect square on the left side: (x + 1.916666667)(x + 1.916666667) = 7.173611112 Calculate the square root of the right side: 2.67835978 Break this problem into two subproblems by setting (x + 1.916666667) equal to 2.67835978 and -2.67835978.Subproblem 1
x + 1.916666667 = 2.67835978 Simplifying x + 1.916666667 = 2.67835978 Reorder the terms: 1.916666667 + x = 2.67835978 Solving 1.916666667 + x = 2.67835978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = 2.67835978 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = 2.67835978 + -1.916666667 x = 2.67835978 + -1.916666667 Combine like terms: 2.67835978 + -1.916666667 = 0.761693113 x = 0.761693113 Simplifying x = 0.761693113Subproblem 2
x + 1.916666667 = -2.67835978 Simplifying x + 1.916666667 = -2.67835978 Reorder the terms: 1.916666667 + x = -2.67835978 Solving 1.916666667 + x = -2.67835978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + x = -2.67835978 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + x = -2.67835978 + -1.916666667 x = -2.67835978 + -1.916666667 Combine like terms: -2.67835978 + -1.916666667 = -4.595026447 x = -4.595026447 Simplifying x = -4.595026447Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.761693113, -4.595026447}Solution
x = {0.761693113, -4.595026447}
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