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Simplifying 10x2 + -52x + 60 = 0 Reorder the terms: 60 + -52x + 10x2 = 0 Solving 60 + -52x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(30 + -26x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + -26x + 5x2)' equal to zero and attempt to solve: Simplifying 30 + -26x + 5x2 = 0 Solving 30 + -26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6 + -5.2x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -5.2x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -5.2x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5.2x + x2 = 0 + -6 -5.2x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -5.2x + x2 = -6 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = -6 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = -6 + 6.76 Combine like terms: -6 + 6.76 = 0.76 6.76 + -5.2x + x2 = 0.76 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (x + -2.6) equal to 0.871779789 and -0.871779789.Subproblem 1
x + -2.6 = 0.871779789 Simplifying x + -2.6 = 0.871779789 Reorder the terms: -2.6 + x = 0.871779789 Solving -2.6 + x = 0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 0.871779789 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 0.871779789 + 2.6 x = 0.871779789 + 2.6 Combine like terms: 0.871779789 + 2.6 = 3.471779789 x = 3.471779789 Simplifying x = 3.471779789Subproblem 2
x + -2.6 = -0.871779789 Simplifying x + -2.6 = -0.871779789 Reorder the terms: -2.6 + x = -0.871779789 Solving -2.6 + x = -0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -0.871779789 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -0.871779789 + 2.6 x = -0.871779789 + 2.6 Combine like terms: -0.871779789 + 2.6 = 1.728220211 x = 1.728220211 Simplifying x = 1.728220211Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.471779789, 1.728220211}Solution
x = {3.471779789, 1.728220211}
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