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Simplifying 2x2 + -46x + 60 = 0 Reorder the terms: 60 + -46x + 2x2 = 0 Solving 60 + -46x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(30 + -23x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + -23x + x2)' equal to zero and attempt to solve: Simplifying 30 + -23x + x2 = 0 Solving 30 + -23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -23x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -23x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -23x + x2 = 0 + -30 -23x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -23x + x2 = -30 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -30 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -30 + 132.25 Combine like terms: -30 + 132.25 = 102.25 132.25 + -23x + x2 = 102.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (x + -11.5) equal to 10.111874208 and -10.111874208.Subproblem 1
x + -11.5 = 10.111874208 Simplifying x + -11.5 = 10.111874208 Reorder the terms: -11.5 + x = 10.111874208 Solving -11.5 + x = 10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 10.111874208 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 10.111874208 + 11.5 x = 10.111874208 + 11.5 Combine like terms: 10.111874208 + 11.5 = 21.611874208 x = 21.611874208 Simplifying x = 21.611874208Subproblem 2
x + -11.5 = -10.111874208 Simplifying x + -11.5 = -10.111874208 Reorder the terms: -11.5 + x = -10.111874208 Solving -11.5 + x = -10.111874208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -10.111874208 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -10.111874208 + 11.5 x = -10.111874208 + 11.5 Combine like terms: -10.111874208 + 11.5 = 1.388125792 x = 1.388125792 Simplifying x = 1.388125792Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.611874208, 1.388125792}Solution
x = {21.611874208, 1.388125792}
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