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Simplifying 36x2 + -24x = 41 Reorder the terms: -24x + 36x2 = 41 Solving -24x + 36x2 = 41 Solving for variable 'x'. Reorder the terms: -41 + -24x + 36x2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + -24x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1.138888889 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '1.138888889' to each side of the equation. -1.138888889 + -0.6666666667x + 1.138888889 + x2 = 0 + 1.138888889 Reorder the terms: -1.138888889 + 1.138888889 + -0.6666666667x + x2 = 0 + 1.138888889 Combine like terms: -1.138888889 + 1.138888889 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + 1.138888889 -0.6666666667x + x2 = 0 + 1.138888889 Combine like terms: 0 + 1.138888889 = 1.138888889 -0.6666666667x + x2 = 1.138888889 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 = 1.138888889 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 1.138888889 + 0.1111111112 Combine like terms: 1.138888889 + 0.1111111112 = 1.2500000002 0.1111111112 + -0.6666666667x + x2 = 1.2500000002 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 1.2500000002 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -0.3333333334 = 1.118033989 Simplifying x + -0.3333333334 = 1.118033989 Reorder the terms: -0.3333333334 + x = 1.118033989 Solving -0.3333333334 + x = 1.118033989 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 = 1.118033989 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 1.118033989 + 0.3333333334 x = 1.118033989 + 0.3333333334 Combine like terms: 1.118033989 + 0.3333333334 = 1.4513673224 x = 1.4513673224 Simplifying x = 1.4513673224Subproblem 2
x + -0.3333333334 = -1.118033989 Simplifying x + -0.3333333334 = -1.118033989 Reorder the terms: -0.3333333334 + x = -1.118033989 Solving -0.3333333334 + x = -1.118033989 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 = -1.118033989 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -1.118033989 + 0.3333333334 x = -1.118033989 + 0.3333333334 Combine like terms: -1.118033989 + 0.3333333334 = -0.7847006556 x = -0.7847006556 Simplifying x = -0.7847006556Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4513673224, -0.7847006556}
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