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Simplifying 9x2 + 24x = 64 Reorder the terms: 24x + 9x2 = 64 Solving 24x + 9x2 = 64 Solving for variable 'x'. Reorder the terms: -64 + 24x + 9x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -7.111111111 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '7.111111111' to each side of the equation. -7.111111111 + 2.666666667x + 7.111111111 + x2 = 0 + 7.111111111 Reorder the terms: -7.111111111 + 7.111111111 + 2.666666667x + x2 = 0 + 7.111111111 Combine like terms: -7.111111111 + 7.111111111 = 0.000000000 0.000000000 + 2.666666667x + x2 = 0 + 7.111111111 2.666666667x + x2 = 0 + 7.111111111 Combine like terms: 0 + 7.111111111 = 7.111111111 2.666666667x + x2 = 7.111111111 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = 7.111111111 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = 7.111111111 + 1.777777780 Combine like terms: 7.111111111 + 1.777777780 = 8.888888891 1.777777780 + 2.666666667x + x2 = 8.888888891 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = 8.888888891 Calculate the square root of the right side: 2.98142397 Break this problem into two subproblems by setting (x + 1.333333334) equal to 2.98142397 and -2.98142397.Subproblem 1
x + 1.333333334 = 2.98142397 Simplifying x + 1.333333334 = 2.98142397 Reorder the terms: 1.333333334 + x = 2.98142397 Solving 1.333333334 + x = 2.98142397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 2.98142397 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 2.98142397 + -1.333333334 x = 2.98142397 + -1.333333334 Combine like terms: 2.98142397 + -1.333333334 = 1.648090636 x = 1.648090636 Simplifying x = 1.648090636Subproblem 2
x + 1.333333334 = -2.98142397 Simplifying x + 1.333333334 = -2.98142397 Reorder the terms: 1.333333334 + x = -2.98142397 Solving 1.333333334 + x = -2.98142397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -2.98142397 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -2.98142397 + -1.333333334 x = -2.98142397 + -1.333333334 Combine like terms: -2.98142397 + -1.333333334 = -4.314757304 x = -4.314757304 Simplifying x = -4.314757304Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.648090636, -4.314757304}
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