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Simplifying 12x2 + x + -70 = 0 Reorder the terms: -70 + x + 12x2 = 0 Solving -70 + x + 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'. -5.833333333 + 0.08333333333x + x2 = 0 Move the constant term to the right: Add '5.833333333' to each side of the equation. -5.833333333 + 0.08333333333x + 5.833333333 + x2 = 0 + 5.833333333 Reorder the terms: -5.833333333 + 5.833333333 + 0.08333333333x + x2 = 0 + 5.833333333 Combine like terms: -5.833333333 + 5.833333333 = 0.000000000 0.000000000 + 0.08333333333x + x2 = 0 + 5.833333333 0.08333333333x + x2 = 0 + 5.833333333 Combine like terms: 0 + 5.833333333 = 5.833333333 0.08333333333x + x2 = 5.833333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.08333333333x + 0.25 + x2 = 5.833333333 + 0.25 Reorder the terms: 0.25 + 0.08333333333x + x2 = 5.833333333 + 0.25 Combine like terms: 5.833333333 + 0.25 = 6.083333333 0.25 + 0.08333333333x + x2 = 6.083333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 6.083333333 Calculate the square root of the right side: 2.466441431 Break this problem into two subproblems by setting (x + 0.5) equal to 2.466441431 and -2.466441431.Subproblem 1
x + 0.5 = 2.466441431 Simplifying x + 0.5 = 2.466441431 Reorder the terms: 0.5 + x = 2.466441431 Solving 0.5 + x = 2.466441431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.466441431 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.466441431 + -0.5 x = 2.466441431 + -0.5 Combine like terms: 2.466441431 + -0.5 = 1.966441431 x = 1.966441431 Simplifying x = 1.966441431Subproblem 2
x + 0.5 = -2.466441431 Simplifying x + 0.5 = -2.466441431 Reorder the terms: 0.5 + x = -2.466441431 Solving 0.5 + x = -2.466441431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.466441431 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.466441431 + -0.5 x = -2.466441431 + -0.5 Combine like terms: -2.466441431 + -0.5 = -2.966441431 x = -2.966441431 Simplifying x = -2.966441431Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.966441431, -2.966441431}
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