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Simplifying 5x2 + -105x + 30 = 0 Reorder the terms: 30 + -105x + 5x2 = 0 Solving 30 + -105x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(6 + -21x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + -21x + x2)' equal to zero and attempt to solve: Simplifying 6 + -21x + x2 = 0 Solving 6 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -21x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -21x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -21x + x2 = 0 + -6 -21x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -21x + x2 = -6 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -6 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -6 + 110.25 Combine like terms: -6 + 110.25 = 104.25 110.25 + -21x + x2 = 104.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (x + -10.5) equal to 10.210288928 and -10.210288928.Subproblem 1
x + -10.5 = 10.210288928 Simplifying x + -10.5 = 10.210288928 Reorder the terms: -10.5 + x = 10.210288928 Solving -10.5 + x = 10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 10.210288928 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 10.210288928 + 10.5 x = 10.210288928 + 10.5 Combine like terms: 10.210288928 + 10.5 = 20.710288928 x = 20.710288928 Simplifying x = 20.710288928Subproblem 2
x + -10.5 = -10.210288928 Simplifying x + -10.5 = -10.210288928 Reorder the terms: -10.5 + x = -10.210288928 Solving -10.5 + x = -10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -10.210288928 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -10.210288928 + 10.5 x = -10.210288928 + 10.5 Combine like terms: -10.210288928 + 10.5 = 0.289711072 x = 0.289711072 Simplifying x = 0.289711072Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.710288928, 0.289711072}Solution
x = {20.710288928, 0.289711072}
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