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Simplifying 6x2 + 34x + 4 = 0 Reorder the terms: 4 + 34x + 6x2 = 0 Solving 4 + 34x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 17x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 17x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + 17x + 3x2 = 0 Solving 2 + 17x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 5.666666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 5.666666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 5.666666667x + x2 = 0 + -0.6666666667 5.666666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 5.666666667x + x2 = -0.6666666667 The x term is 5.666666667x. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667x + 8.027777782 + x2 = -0.6666666667 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = -0.6666666667 + 8.027777782 Combine like terms: -0.6666666667 + 8.027777782 = 7.3611111153 8.027777782 + 5.666666667x + x2 = 7.3611111153 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 7.3611111153 Calculate the square root of the right side: 2.713136767 Break this problem into two subproblems by setting (x + 2.833333334) equal to 2.713136767 and -2.713136767.Subproblem 1
x + 2.833333334 = 2.713136767 Simplifying x + 2.833333334 = 2.713136767 Reorder the terms: 2.833333334 + x = 2.713136767 Solving 2.833333334 + x = 2.713136767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = 2.713136767 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 2.713136767 + -2.833333334 x = 2.713136767 + -2.833333334 Combine like terms: 2.713136767 + -2.833333334 = -0.120196567 x = -0.120196567 Simplifying x = -0.120196567Subproblem 2
x + 2.833333334 = -2.713136767 Simplifying x + 2.833333334 = -2.713136767 Reorder the terms: 2.833333334 + x = -2.713136767 Solving 2.833333334 + x = -2.713136767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = -2.713136767 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -2.713136767 + -2.833333334 x = -2.713136767 + -2.833333334 Combine like terms: -2.713136767 + -2.833333334 = -5.546470101 x = -5.546470101 Simplifying x = -5.546470101Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.120196567, -5.546470101}Solution
x = {-0.120196567, -5.546470101}
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