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Simplifying 9x2 + -37 = 6x Reorder the terms: -37 + 9x2 = 6x Solving -37 + 9x2 = 6x Solving for variable 'x'. Reorder the terms: -37 + -6x + 9x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -37 + -6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4.111111111 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '4.111111111' to each side of the equation. -4.111111111 + -0.6666666667x + 4.111111111 + x2 = 0 + 4.111111111 Reorder the terms: -4.111111111 + 4.111111111 + -0.6666666667x + x2 = 0 + 4.111111111 Combine like terms: -4.111111111 + 4.111111111 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + 4.111111111 -0.6666666667x + x2 = 0 + 4.111111111 Combine like terms: 0 + 4.111111111 = 4.111111111 -0.6666666667x + x2 = 4.111111111 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 = 4.111111111 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 4.111111111 + 0.1111111112 Combine like terms: 4.111111111 + 0.1111111112 = 4.2222222222 0.1111111112 + -0.6666666667x + x2 = 4.2222222222 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 4.2222222222 Calculate the square root of the right side: 2.054804668 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 2.054804668 and -2.054804668.Subproblem 1
x + -0.3333333334 = 2.054804668 Simplifying x + -0.3333333334 = 2.054804668 Reorder the terms: -0.3333333334 + x = 2.054804668 Solving -0.3333333334 + x = 2.054804668 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 = 2.054804668 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 2.054804668 + 0.3333333334 x = 2.054804668 + 0.3333333334 Combine like terms: 2.054804668 + 0.3333333334 = 2.3881380014 x = 2.3881380014 Simplifying x = 2.3881380014Subproblem 2
x + -0.3333333334 = -2.054804668 Simplifying x + -0.3333333334 = -2.054804668 Reorder the terms: -0.3333333334 + x = -2.054804668 Solving -0.3333333334 + x = -2.054804668 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 = -2.054804668 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -2.054804668 + 0.3333333334 x = -2.054804668 + 0.3333333334 Combine like terms: -2.054804668 + 0.3333333334 = -1.7214713346 x = -1.7214713346 Simplifying x = -1.7214713346Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3881380014, -1.7214713346}
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