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Simplifying 12x2 + -481x + -1270 = 0 Reorder the terms: -1270 + -481x + 12x2 = 0 Solving -1270 + -481x + 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'. -105.8333333 + -40.08333333x + x2 = 0 Move the constant term to the right: Add '105.8333333' to each side of the equation. -105.8333333 + -40.08333333x + 105.8333333 + x2 = 0 + 105.8333333 Reorder the terms: -105.8333333 + 105.8333333 + -40.08333333x + x2 = 0 + 105.8333333 Combine like terms: -105.8333333 + 105.8333333 = 0.0000000 0.0000000 + -40.08333333x + x2 = 0 + 105.8333333 -40.08333333x + x2 = 0 + 105.8333333 Combine like terms: 0 + 105.8333333 = 105.8333333 -40.08333333x + x2 = 105.8333333 The x term is -40.08333333x. Take half its coefficient (-20.04166667). Square it (401.6684029) and add it to both sides. Add '401.6684029' to each side of the equation. -40.08333333x + 401.6684029 + x2 = 105.8333333 + 401.6684029 Reorder the terms: 401.6684029 + -40.08333333x + x2 = 105.8333333 + 401.6684029 Combine like terms: 105.8333333 + 401.6684029 = 507.5017362 401.6684029 + -40.08333333x + x2 = 507.5017362 Factor a perfect square on the left side: (x + -20.04166667)(x + -20.04166667) = 507.5017362 Calculate the square root of the right side: 22.527799187 Break this problem into two subproblems by setting (x + -20.04166667) equal to 22.527799187 and -22.527799187.Subproblem 1
x + -20.04166667 = 22.527799187 Simplifying x + -20.04166667 = 22.527799187 Reorder the terms: -20.04166667 + x = 22.527799187 Solving -20.04166667 + x = 22.527799187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.04166667' to each side of the equation. -20.04166667 + 20.04166667 + x = 22.527799187 + 20.04166667 Combine like terms: -20.04166667 + 20.04166667 = 0.00000000 0.00000000 + x = 22.527799187 + 20.04166667 x = 22.527799187 + 20.04166667 Combine like terms: 22.527799187 + 20.04166667 = 42.569465857 x = 42.569465857 Simplifying x = 42.569465857Subproblem 2
x + -20.04166667 = -22.527799187 Simplifying x + -20.04166667 = -22.527799187 Reorder the terms: -20.04166667 + x = -22.527799187 Solving -20.04166667 + x = -22.527799187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.04166667' to each side of the equation. -20.04166667 + 20.04166667 + x = -22.527799187 + 20.04166667 Combine like terms: -20.04166667 + 20.04166667 = 0.00000000 0.00000000 + x = -22.527799187 + 20.04166667 x = -22.527799187 + 20.04166667 Combine like terms: -22.527799187 + 20.04166667 = -2.486132517 x = -2.486132517 Simplifying x = -2.486132517Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.569465857, -2.486132517}
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