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Simplifying 6(x + 9) = 5(5x + -8) * x Reorder the terms: 6(9 + x) = 5(5x + -8) * x (9 * 6 + x * 6) = 5(5x + -8) * x (54 + 6x) = 5(5x + -8) * x Reorder the terms: 54 + 6x = 5(-8 + 5x) * x Reorder the terms for easier multiplication: 54 + 6x = 5x(-8 + 5x) 54 + 6x = (-8 * 5x + 5x * 5x) 54 + 6x = (-40x + 25x2) Solving 54 + 6x = -40x + 25x2 Solving for variable 'x'. Combine like terms: 6x + 40x = 46x 54 + 46x + -25x2 = -40x + 25x2 + 40x + -25x2 Reorder the terms: 54 + 46x + -25x2 = -40x + 40x + 25x2 + -25x2 Combine like terms: -40x + 40x = 0 54 + 46x + -25x2 = 0 + 25x2 + -25x2 54 + 46x + -25x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 54 + 46x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -2.16 + -1.84x + x2 = 0 Move the constant term to the right: Add '2.16' to each side of the equation. -2.16 + -1.84x + 2.16 + x2 = 0 + 2.16 Reorder the terms: -2.16 + 2.16 + -1.84x + x2 = 0 + 2.16 Combine like terms: -2.16 + 2.16 = 0.00 0.00 + -1.84x + x2 = 0 + 2.16 -1.84x + x2 = 0 + 2.16 Combine like terms: 0 + 2.16 = 2.16 -1.84x + x2 = 2.16 The x term is -1.84x. Take half its coefficient (-0.92). Square it (0.8464) and add it to both sides. Add '0.8464' to each side of the equation. -1.84x + 0.8464 + x2 = 2.16 + 0.8464 Reorder the terms: 0.8464 + -1.84x + x2 = 2.16 + 0.8464 Combine like terms: 2.16 + 0.8464 = 3.0064 0.8464 + -1.84x + x2 = 3.0064 Factor a perfect square on the left side: (x + -0.92)(x + -0.92) = 3.0064 Calculate the square root of the right side: 1.733897344 Break this problem into two subproblems by setting (x + -0.92) equal to 1.733897344 and -1.733897344.Subproblem 1
x + -0.92 = 1.733897344 Simplifying x + -0.92 = 1.733897344 Reorder the terms: -0.92 + x = 1.733897344 Solving -0.92 + x = 1.733897344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.92' to each side of the equation. -0.92 + 0.92 + x = 1.733897344 + 0.92 Combine like terms: -0.92 + 0.92 = 0.00 0.00 + x = 1.733897344 + 0.92 x = 1.733897344 + 0.92 Combine like terms: 1.733897344 + 0.92 = 2.653897344 x = 2.653897344 Simplifying x = 2.653897344Subproblem 2
x + -0.92 = -1.733897344 Simplifying x + -0.92 = -1.733897344 Reorder the terms: -0.92 + x = -1.733897344 Solving -0.92 + x = -1.733897344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.92' to each side of the equation. -0.92 + 0.92 + x = -1.733897344 + 0.92 Combine like terms: -0.92 + 0.92 = 0.00 0.00 + x = -1.733897344 + 0.92 x = -1.733897344 + 0.92 Combine like terms: -1.733897344 + 0.92 = -0.813897344 x = -0.813897344 Simplifying x = -0.813897344Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.653897344, -0.813897344}
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