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Simplifying 12x2 + -2x + -15 = 0 Reorder the terms: -15 + -2x + 12x2 = 0 Solving -15 + -2x + 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'. -1.25 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -0.1666666667x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -0.1666666667x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.1666666667x + x2 = 0 + 1.25 -0.1666666667x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -0.1666666667x + x2 = 1.25 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 1.25 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 1.25 + 0.006944444447 Combine like terms: 1.25 + 0.006944444447 = 1.256944444447 0.006944444447 + -0.1666666667x + x2 = 1.256944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 1.256944444447 Calculate the square root of the right side: 1.121135337 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 1.121135337 and -1.121135337.Subproblem 1
x + -0.08333333335 = 1.121135337 Simplifying x + -0.08333333335 = 1.121135337 Reorder the terms: -0.08333333335 + x = 1.121135337 Solving -0.08333333335 + x = 1.121135337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 1.121135337 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 1.121135337 + 0.08333333335 x = 1.121135337 + 0.08333333335 Combine like terms: 1.121135337 + 0.08333333335 = 1.20446867035 x = 1.20446867035 Simplifying x = 1.20446867035Subproblem 2
x + -0.08333333335 = -1.121135337 Simplifying x + -0.08333333335 = -1.121135337 Reorder the terms: -0.08333333335 + x = -1.121135337 Solving -0.08333333335 + x = -1.121135337 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -1.121135337 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -1.121135337 + 0.08333333335 x = -1.121135337 + 0.08333333335 Combine like terms: -1.121135337 + 0.08333333335 = -1.03780200365 x = -1.03780200365 Simplifying x = -1.03780200365Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.20446867035, -1.03780200365}
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