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Simplifying 36x2 + 24x + -13 = 0 Reorder the terms: -13 + 24x + 36x2 = 0 Solving -13 + 24x + 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'. -0.3611111111 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.3611111111' to each side of the equation. -0.3611111111 + 0.6666666667x + 0.3611111111 + x2 = 0 + 0.3611111111 Reorder the terms: -0.3611111111 + 0.3611111111 + 0.6666666667x + x2 = 0 + 0.3611111111 Combine like terms: -0.3611111111 + 0.3611111111 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + 0.3611111111 0.6666666667x + x2 = 0 + 0.3611111111 Combine like terms: 0 + 0.3611111111 = 0.3611111111 0.6666666667x + x2 = 0.3611111111 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.3611111111 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.3611111111 + 0.1111111112 Combine like terms: 0.3611111111 + 0.1111111112 = 0.4722222223 0.1111111112 + 0.6666666667x + x2 = 0.4722222223 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.4722222223 Calculate the square root of the right side: 0.687184271 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.687184271 and -0.687184271.Subproblem 1
x + 0.3333333334 = 0.687184271 Simplifying x + 0.3333333334 = 0.687184271 Reorder the terms: 0.3333333334 + x = 0.687184271 Solving 0.3333333334 + x = 0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.687184271 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.687184271 + -0.3333333334 x = 0.687184271 + -0.3333333334 Combine like terms: 0.687184271 + -0.3333333334 = 0.3538509376 x = 0.3538509376 Simplifying x = 0.3538509376Subproblem 2
x + 0.3333333334 = -0.687184271 Simplifying x + 0.3333333334 = -0.687184271 Reorder the terms: 0.3333333334 + x = -0.687184271 Solving 0.3333333334 + x = -0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.687184271 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.687184271 + -0.3333333334 x = -0.687184271 + -0.3333333334 Combine like terms: -0.687184271 + -0.3333333334 = -1.0205176044 x = -1.0205176044 Simplifying x = -1.0205176044Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3538509376, -1.0205176044}
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