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Simplifying 3x2 + 3x2 + 4x + 10x + -100x + 10 = 0 Reorder the terms: 10 + 4x + 10x + -100x + 3x2 + 3x2 = 0 Combine like terms: 4x + 10x = 14x 10 + 14x + -100x + 3x2 + 3x2 = 0 Combine like terms: 14x + -100x = -86x 10 + -86x + 3x2 + 3x2 = 0 Combine like terms: 3x2 + 3x2 = 6x2 10 + -86x + 6x2 = 0 Solving 10 + -86x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -43x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -43x + 3x2)' equal to zero and attempt to solve: Simplifying 5 + -43x + 3x2 = 0 Solving 5 + -43x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -14.33333333x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -14.33333333x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -14.33333333x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -14.33333333x + x2 = 0 + -1.666666667 -14.33333333x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -14.33333333x + x2 = -1.666666667 The x term is -14.33333333x. Take half its coefficient (-7.166666665). Square it (51.36111109) and add it to both sides. Add '51.36111109' to each side of the equation. -14.33333333x + 51.36111109 + x2 = -1.666666667 + 51.36111109 Reorder the terms: 51.36111109 + -14.33333333x + x2 = -1.666666667 + 51.36111109 Combine like terms: -1.666666667 + 51.36111109 = 49.694444423 51.36111109 + -14.33333333x + x2 = 49.694444423 Factor a perfect square on the left side: (x + -7.166666665)(x + -7.166666665) = 49.694444423 Calculate the square root of the right side: 7.049428659 Break this problem into two subproblems by setting (x + -7.166666665) equal to 7.049428659 and -7.049428659.Subproblem 1
x + -7.166666665 = 7.049428659 Simplifying x + -7.166666665 = 7.049428659 Reorder the terms: -7.166666665 + x = 7.049428659 Solving -7.166666665 + x = 7.049428659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.166666665' to each side of the equation. -7.166666665 + 7.166666665 + x = 7.049428659 + 7.166666665 Combine like terms: -7.166666665 + 7.166666665 = 0.000000000 0.000000000 + x = 7.049428659 + 7.166666665 x = 7.049428659 + 7.166666665 Combine like terms: 7.049428659 + 7.166666665 = 14.216095324 x = 14.216095324 Simplifying x = 14.216095324Subproblem 2
x + -7.166666665 = -7.049428659 Simplifying x + -7.166666665 = -7.049428659 Reorder the terms: -7.166666665 + x = -7.049428659 Solving -7.166666665 + x = -7.049428659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.166666665' to each side of the equation. -7.166666665 + 7.166666665 + x = -7.049428659 + 7.166666665 Combine like terms: -7.166666665 + 7.166666665 = 0.000000000 0.000000000 + x = -7.049428659 + 7.166666665 x = -7.049428659 + 7.166666665 Combine like terms: -7.049428659 + 7.166666665 = 0.117238006 x = 0.117238006 Simplifying x = 0.117238006Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.216095324, 0.117238006}Solution
x = {14.216095324, 0.117238006}
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