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Simplifying 30x2 + -928x + 6 = 0 Reorder the terms: 6 + -928x + 30x2 = 0 Solving 6 + -928x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -464x + 15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -464x + 15x2)' equal to zero and attempt to solve: Simplifying 3 + -464x + 15x2 = 0 Solving 3 + -464x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.2 + -30.93333333x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -30.93333333x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -30.93333333x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -30.93333333x + x2 = 0 + -0.2 -30.93333333x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -30.93333333x + x2 = -0.2 The x term is -30.93333333x. Take half its coefficient (-15.46666667). Square it (239.2177779) and add it to both sides. Add '239.2177779' to each side of the equation. -30.93333333x + 239.2177779 + x2 = -0.2 + 239.2177779 Reorder the terms: 239.2177779 + -30.93333333x + x2 = -0.2 + 239.2177779 Combine like terms: -0.2 + 239.2177779 = 239.0177779 239.2177779 + -30.93333333x + x2 = 239.0177779 Factor a perfect square on the left side: (x + -15.46666667)(x + -15.46666667) = 239.0177779 Calculate the square root of the right side: 15.460199801 Break this problem into two subproblems by setting (x + -15.46666667) equal to 15.460199801 and -15.460199801.Subproblem 1
x + -15.46666667 = 15.460199801 Simplifying x + -15.46666667 = 15.460199801 Reorder the terms: -15.46666667 + x = 15.460199801 Solving -15.46666667 + x = 15.460199801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.46666667' to each side of the equation. -15.46666667 + 15.46666667 + x = 15.460199801 + 15.46666667 Combine like terms: -15.46666667 + 15.46666667 = 0.00000000 0.00000000 + x = 15.460199801 + 15.46666667 x = 15.460199801 + 15.46666667 Combine like terms: 15.460199801 + 15.46666667 = 30.926866471 x = 30.926866471 Simplifying x = 30.926866471Subproblem 2
x + -15.46666667 = -15.460199801 Simplifying x + -15.46666667 = -15.460199801 Reorder the terms: -15.46666667 + x = -15.460199801 Solving -15.46666667 + x = -15.460199801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.46666667' to each side of the equation. -15.46666667 + 15.46666667 + x = -15.460199801 + 15.46666667 Combine like terms: -15.46666667 + 15.46666667 = 0.00000000 0.00000000 + x = -15.460199801 + 15.46666667 x = -15.460199801 + 15.46666667 Combine like terms: -15.460199801 + 15.46666667 = 0.006466869 x = 0.006466869 Simplifying x = 0.006466869Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.926866471, 0.006466869}Solution
x = {30.926866471, 0.006466869}
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