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Simplifying 96x2 + -410x + -60 = 0 Reorder the terms: -60 + -410x + 96x2 = 0 Solving -60 + -410x + 96x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + -205x + 48x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + -205x + 48x2)' equal to zero and attempt to solve: Simplifying -30 + -205x + 48x2 = 0 Solving -30 + -205x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.625 + -4.270833333x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -4.270833333x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -4.270833333x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -4.270833333x + x2 = 0 + 0.625 -4.270833333x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -4.270833333x + x2 = 0.625 The x term is -4.270833333x. Take half its coefficient (-2.135416667). Square it (4.560004342) and add it to both sides. Add '4.560004342' to each side of the equation. -4.270833333x + 4.560004342 + x2 = 0.625 + 4.560004342 Reorder the terms: 4.560004342 + -4.270833333x + x2 = 0.625 + 4.560004342 Combine like terms: 0.625 + 4.560004342 = 5.185004342 4.560004342 + -4.270833333x + x2 = 5.185004342 Factor a perfect square on the left side: (x + -2.135416667)(x + -2.135416667) = 5.185004342 Calculate the square root of the right side: 2.277060461 Break this problem into two subproblems by setting (x + -2.135416667) equal to 2.277060461 and -2.277060461.Subproblem 1
x + -2.135416667 = 2.277060461 Simplifying x + -2.135416667 = 2.277060461 Reorder the terms: -2.135416667 + x = 2.277060461 Solving -2.135416667 + x = 2.277060461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.135416667' to each side of the equation. -2.135416667 + 2.135416667 + x = 2.277060461 + 2.135416667 Combine like terms: -2.135416667 + 2.135416667 = 0.000000000 0.000000000 + x = 2.277060461 + 2.135416667 x = 2.277060461 + 2.135416667 Combine like terms: 2.277060461 + 2.135416667 = 4.412477128 x = 4.412477128 Simplifying x = 4.412477128Subproblem 2
x + -2.135416667 = -2.277060461 Simplifying x + -2.135416667 = -2.277060461 Reorder the terms: -2.135416667 + x = -2.277060461 Solving -2.135416667 + x = -2.277060461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.135416667' to each side of the equation. -2.135416667 + 2.135416667 + x = -2.277060461 + 2.135416667 Combine like terms: -2.135416667 + 2.135416667 = 0.000000000 0.000000000 + x = -2.277060461 + 2.135416667 x = -2.277060461 + 2.135416667 Combine like terms: -2.277060461 + 2.135416667 = -0.141643794 x = -0.141643794 Simplifying x = -0.141643794Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.412477128, -0.141643794}Solution
x = {4.412477128, -0.141643794}
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