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Simplifying 42x2 + -288x + -39 = 0 Reorder the terms: -39 + -288x + 42x2 = 0 Solving -39 + -288x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + -96x + 14x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + -96x + 14x2)' equal to zero and attempt to solve: Simplifying -13 + -96x + 14x2 = 0 Solving -13 + -96x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.9285714286 + -6.857142857x + x2 = 0 Move the constant term to the right: Add '0.9285714286' to each side of the equation. -0.9285714286 + -6.857142857x + 0.9285714286 + x2 = 0 + 0.9285714286 Reorder the terms: -0.9285714286 + 0.9285714286 + -6.857142857x + x2 = 0 + 0.9285714286 Combine like terms: -0.9285714286 + 0.9285714286 = 0.0000000000 0.0000000000 + -6.857142857x + x2 = 0 + 0.9285714286 -6.857142857x + x2 = 0 + 0.9285714286 Combine like terms: 0 + 0.9285714286 = 0.9285714286 -6.857142857x + x2 = 0.9285714286 The x term is -6.857142857x. Take half its coefficient (-3.428571429). Square it (11.75510204) and add it to both sides. Add '11.75510204' to each side of the equation. -6.857142857x + 11.75510204 + x2 = 0.9285714286 + 11.75510204 Reorder the terms: 11.75510204 + -6.857142857x + x2 = 0.9285714286 + 11.75510204 Combine like terms: 0.9285714286 + 11.75510204 = 12.6836734686 11.75510204 + -6.857142857x + x2 = 12.6836734686 Factor a perfect square on the left side: (x + -3.428571429)(x + -3.428571429) = 12.6836734686 Calculate the square root of the right side: 3.561414532 Break this problem into two subproblems by setting (x + -3.428571429) equal to 3.561414532 and -3.561414532.Subproblem 1
x + -3.428571429 = 3.561414532 Simplifying x + -3.428571429 = 3.561414532 Reorder the terms: -3.428571429 + x = 3.561414532 Solving -3.428571429 + x = 3.561414532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.428571429' to each side of the equation. -3.428571429 + 3.428571429 + x = 3.561414532 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = 3.561414532 + 3.428571429 x = 3.561414532 + 3.428571429 Combine like terms: 3.561414532 + 3.428571429 = 6.989985961 x = 6.989985961 Simplifying x = 6.989985961Subproblem 2
x + -3.428571429 = -3.561414532 Simplifying x + -3.428571429 = -3.561414532 Reorder the terms: -3.428571429 + x = -3.561414532 Solving -3.428571429 + x = -3.561414532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.428571429' to each side of the equation. -3.428571429 + 3.428571429 + x = -3.561414532 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = -3.561414532 + 3.428571429 x = -3.561414532 + 3.428571429 Combine like terms: -3.561414532 + 3.428571429 = -0.132843103 x = -0.132843103 Simplifying x = -0.132843103Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.989985961, -0.132843103}Solution
x = {6.989985961, -0.132843103}
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