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Simplifying 12x2 + -2x = 12 Reorder the terms: -2x + 12x2 = 12 Solving -2x + 12x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -2x + 12x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -2x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -1x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -1x + 6x2)' equal to zero and attempt to solve: Simplifying -6 + -1x + 6x2 = 0 Solving -6 + -1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.1666666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.1666666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.1666666667x + x2 = 0 + 1 -0.1666666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.1666666667x + x2 = 1 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 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 1 + 0.006944444447 Combine like terms: 1 + 0.006944444447 = 1.006944444447 0.006944444447 + -0.1666666667x + x2 = 1.006944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 1.006944444447 Calculate the square root of the right side: 1.003466215 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 1.003466215 and -1.003466215.Subproblem 1
x + -0.08333333335 = 1.003466215 Simplifying x + -0.08333333335 = 1.003466215 Reorder the terms: -0.08333333335 + x = 1.003466215 Solving -0.08333333335 + x = 1.003466215 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 = 1.003466215 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 1.003466215 + 0.08333333335 x = 1.003466215 + 0.08333333335 Combine like terms: 1.003466215 + 0.08333333335 = 1.08679954835 x = 1.08679954835 Simplifying x = 1.08679954835Subproblem 2
x + -0.08333333335 = -1.003466215 Simplifying x + -0.08333333335 = -1.003466215 Reorder the terms: -0.08333333335 + x = -1.003466215 Solving -0.08333333335 + x = -1.003466215 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 = -1.003466215 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -1.003466215 + 0.08333333335 x = -1.003466215 + 0.08333333335 Combine like terms: -1.003466215 + 0.08333333335 = -0.92013288165 x = -0.92013288165 Simplifying x = -0.92013288165Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.08679954835, -0.92013288165}Solution
x = {1.08679954835, -0.92013288165}
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