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Simplifying 36x2 + 12x = 13 Reorder the terms: 12x + 36x2 = 13 Solving 12x + 36x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 12x + 36x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 12x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.3611111111 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.3611111111' to each side of the equation. -0.3611111111 + 0.3333333333x + 0.3611111111 + x2 = 0 + 0.3611111111 Reorder the terms: -0.3611111111 + 0.3611111111 + 0.3333333333x + x2 = 0 + 0.3611111111 Combine like terms: -0.3611111111 + 0.3611111111 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + 0.3611111111 0.3333333333x + x2 = 0 + 0.3611111111 Combine like terms: 0 + 0.3611111111 = 0.3611111111 0.3333333333x + x2 = 0.3611111111 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.3611111111 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.3611111111 + 0.02777777779 Combine like terms: 0.3611111111 + 0.02777777779 = 0.38888888889 0.02777777779 + 0.3333333333x + x2 = 0.38888888889 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.38888888889 Calculate the square root of the right side: 0.623609564 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.623609564 and -0.623609564.Subproblem 1
x + 0.1666666667 = 0.623609564 Simplifying x + 0.1666666667 = 0.623609564 Reorder the terms: 0.1666666667 + x = 0.623609564 Solving 0.1666666667 + x = 0.623609564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.623609564 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.623609564 + -0.1666666667 x = 0.623609564 + -0.1666666667 Combine like terms: 0.623609564 + -0.1666666667 = 0.4569428973 x = 0.4569428973 Simplifying x = 0.4569428973Subproblem 2
x + 0.1666666667 = -0.623609564 Simplifying x + 0.1666666667 = -0.623609564 Reorder the terms: 0.1666666667 + x = -0.623609564 Solving 0.1666666667 + x = -0.623609564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.623609564 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.623609564 + -0.1666666667 x = -0.623609564 + -0.1666666667 Combine like terms: -0.623609564 + -0.1666666667 = -0.7902762307 x = -0.7902762307 Simplifying x = -0.7902762307Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4569428973, -0.7902762307}
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