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Simplifying 36x2 + 84x + -49 = 0 Reorder the terms: -49 + 84x + 36x2 = 0 Solving -49 + 84x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1.361111111 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '1.361111111' to each side of the equation. -1.361111111 + 2.333333333x + 1.361111111 + x2 = 0 + 1.361111111 Reorder the terms: -1.361111111 + 1.361111111 + 2.333333333x + x2 = 0 + 1.361111111 Combine like terms: -1.361111111 + 1.361111111 = 0.000000000 0.000000000 + 2.333333333x + x2 = 0 + 1.361111111 2.333333333x + x2 = 0 + 1.361111111 Combine like terms: 0 + 1.361111111 = 1.361111111 2.333333333x + x2 = 1.361111111 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 1.361111111 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 1.361111111 + 1.361111112 Combine like terms: 1.361111111 + 1.361111112 = 2.722222223 1.361111112 + 2.333333333x + x2 = 2.722222223 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 2.722222223 Calculate the square root of the right side: 1.649915823 Break this problem into two subproblems by setting (x + 1.166666667) equal to 1.649915823 and -1.649915823.Subproblem 1
x + 1.166666667 = 1.649915823 Simplifying x + 1.166666667 = 1.649915823 Reorder the terms: 1.166666667 + x = 1.649915823 Solving 1.166666667 + x = 1.649915823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 1.649915823 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 1.649915823 + -1.166666667 x = 1.649915823 + -1.166666667 Combine like terms: 1.649915823 + -1.166666667 = 0.483249156 x = 0.483249156 Simplifying x = 0.483249156Subproblem 2
x + 1.166666667 = -1.649915823 Simplifying x + 1.166666667 = -1.649915823 Reorder the terms: 1.166666667 + x = -1.649915823 Solving 1.166666667 + x = -1.649915823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -1.649915823 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -1.649915823 + -1.166666667 x = -1.649915823 + -1.166666667 Combine like terms: -1.649915823 + -1.166666667 = -2.81658249 x = -2.81658249 Simplifying x = -2.81658249Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.483249156, -2.81658249}
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