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Simplifying 12x2 + 7x + -60 = 0 Reorder the terms: -60 + 7x + 12x2 = 0 Solving -60 + 7x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -5 + 0.5833333333x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.5833333333x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 0.5833333333x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.5833333333x + x2 = 0 + 5 0.5833333333x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.5833333333x + x2 = 5 The x term is 0.5833333333x. Take half its coefficient (0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. 0.5833333333x + 0.08506944446 + x2 = 5 + 0.08506944446 Reorder the terms: 0.08506944446 + 0.5833333333x + x2 = 5 + 0.08506944446 Combine like terms: 5 + 0.08506944446 = 5.08506944446 0.08506944446 + 0.5833333333x + x2 = 5.08506944446 Factor a perfect square on the left side: (x + 0.2916666667)(x + 0.2916666667) = 5.08506944446 Calculate the square root of the right side: 2.255009855 Break this problem into two subproblems by setting (x + 0.2916666667) equal to 2.255009855 and -2.255009855.Subproblem 1
x + 0.2916666667 = 2.255009855 Simplifying x + 0.2916666667 = 2.255009855 Reorder the terms: 0.2916666667 + x = 2.255009855 Solving 0.2916666667 + x = 2.255009855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2916666667' to each side of the equation. 0.2916666667 + -0.2916666667 + x = 2.255009855 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = 2.255009855 + -0.2916666667 x = 2.255009855 + -0.2916666667 Combine like terms: 2.255009855 + -0.2916666667 = 1.9633431883 x = 1.9633431883 Simplifying x = 1.9633431883Subproblem 2
x + 0.2916666667 = -2.255009855 Simplifying x + 0.2916666667 = -2.255009855 Reorder the terms: 0.2916666667 + x = -2.255009855 Solving 0.2916666667 + x = -2.255009855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2916666667' to each side of the equation. 0.2916666667 + -0.2916666667 + x = -2.255009855 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = -2.255009855 + -0.2916666667 x = -2.255009855 + -0.2916666667 Combine like terms: -2.255009855 + -0.2916666667 = -2.5466765217 x = -2.5466765217 Simplifying x = -2.5466765217Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9633431883, -2.5466765217}
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