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Simplifying 52x2 + -238x + 30 = 0 Reorder the terms: 30 + -238x + 52x2 = 0 Solving 30 + -238x + 52x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -119x + 26x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -119x + 26x2)' equal to zero and attempt to solve: Simplifying 15 + -119x + 26x2 = 0 Solving 15 + -119x + 26x2 = 0 Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. 0.5769230769 + -4.576923077x + x2 = 0 Move the constant term to the right: Add '-0.5769230769' to each side of the equation. 0.5769230769 + -4.576923077x + -0.5769230769 + x2 = 0 + -0.5769230769 Reorder the terms: 0.5769230769 + -0.5769230769 + -4.576923077x + x2 = 0 + -0.5769230769 Combine like terms: 0.5769230769 + -0.5769230769 = 0.0000000000 0.0000000000 + -4.576923077x + x2 = 0 + -0.5769230769 -4.576923077x + x2 = 0 + -0.5769230769 Combine like terms: 0 + -0.5769230769 = -0.5769230769 -4.576923077x + x2 = -0.5769230769 The x term is -4.576923077x. Take half its coefficient (-2.288461539). Square it (5.237056215) and add it to both sides. Add '5.237056215' to each side of the equation. -4.576923077x + 5.237056215 + x2 = -0.5769230769 + 5.237056215 Reorder the terms: 5.237056215 + -4.576923077x + x2 = -0.5769230769 + 5.237056215 Combine like terms: -0.5769230769 + 5.237056215 = 4.6601331381 5.237056215 + -4.576923077x + x2 = 4.6601331381 Factor a perfect square on the left side: (x + -2.288461539)(x + -2.288461539) = 4.6601331381 Calculate the square root of the right side: 2.158734152 Break this problem into two subproblems by setting (x + -2.288461539) equal to 2.158734152 and -2.158734152.Subproblem 1
x + -2.288461539 = 2.158734152 Simplifying x + -2.288461539 = 2.158734152 Reorder the terms: -2.288461539 + x = 2.158734152 Solving -2.288461539 + x = 2.158734152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.288461539' to each side of the equation. -2.288461539 + 2.288461539 + x = 2.158734152 + 2.288461539 Combine like terms: -2.288461539 + 2.288461539 = 0.000000000 0.000000000 + x = 2.158734152 + 2.288461539 x = 2.158734152 + 2.288461539 Combine like terms: 2.158734152 + 2.288461539 = 4.447195691 x = 4.447195691 Simplifying x = 4.447195691Subproblem 2
x + -2.288461539 = -2.158734152 Simplifying x + -2.288461539 = -2.158734152 Reorder the terms: -2.288461539 + x = -2.158734152 Solving -2.288461539 + x = -2.158734152 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.288461539' to each side of the equation. -2.288461539 + 2.288461539 + x = -2.158734152 + 2.288461539 Combine like terms: -2.288461539 + 2.288461539 = 0.000000000 0.000000000 + x = -2.158734152 + 2.288461539 x = -2.158734152 + 2.288461539 Combine like terms: -2.158734152 + 2.288461539 = 0.129727387 x = 0.129727387 Simplifying x = 0.129727387Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.447195691, 0.129727387}Solution
x = {4.447195691, 0.129727387}
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