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Simplifying x(25x + 9) = 18 Reorder the terms: x(9 + 25x) = 18 (9 * x + 25x * x) = 18 (9x + 25x2) = 18 Solving 9x + 25x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 9x + 25x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 9x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.72 + 0.36x + x2 = 0 Move the constant term to the right: Add '0.72' to each side of the equation. -0.72 + 0.36x + 0.72 + x2 = 0 + 0.72 Reorder the terms: -0.72 + 0.72 + 0.36x + x2 = 0 + 0.72 Combine like terms: -0.72 + 0.72 = 0.00 0.00 + 0.36x + x2 = 0 + 0.72 0.36x + x2 = 0 + 0.72 Combine like terms: 0 + 0.72 = 0.72 0.36x + x2 = 0.72 The x term is 0.36x. Take half its coefficient (0.18). Square it (0.0324) and add it to both sides. Add '0.0324' to each side of the equation. 0.36x + 0.0324 + x2 = 0.72 + 0.0324 Reorder the terms: 0.0324 + 0.36x + x2 = 0.72 + 0.0324 Combine like terms: 0.72 + 0.0324 = 0.7524 0.0324 + 0.36x + x2 = 0.7524 Factor a perfect square on the left side: (x + 0.18)(x + 0.18) = 0.7524 Calculate the square root of the right side: 0.867409938 Break this problem into two subproblems by setting (x + 0.18) equal to 0.867409938 and -0.867409938.Subproblem 1
x + 0.18 = 0.867409938 Simplifying x + 0.18 = 0.867409938 Reorder the terms: 0.18 + x = 0.867409938 Solving 0.18 + x = 0.867409938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.18' to each side of the equation. 0.18 + -0.18 + x = 0.867409938 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 0.00 + x = 0.867409938 + -0.18 x = 0.867409938 + -0.18 Combine like terms: 0.867409938 + -0.18 = 0.687409938 x = 0.687409938 Simplifying x = 0.687409938Subproblem 2
x + 0.18 = -0.867409938 Simplifying x + 0.18 = -0.867409938 Reorder the terms: 0.18 + x = -0.867409938 Solving 0.18 + x = -0.867409938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.18' to each side of the equation. 0.18 + -0.18 + x = -0.867409938 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 0.00 + x = -0.867409938 + -0.18 x = -0.867409938 + -0.18 Combine like terms: -0.867409938 + -0.18 = -1.047409938 x = -1.047409938 Simplifying x = -1.047409938Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.687409938, -1.047409938}
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