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Simplifying 8x(4 + 2x) = 9x + 17 (4 * 8x + 2x * 8x) = 9x + 17 (32x + 16x2) = 9x + 17 Reorder the terms: 32x + 16x2 = 17 + 9x Solving 32x + 16x2 = 17 + 9x Solving for variable 'x'. Reorder the terms: -17 + 32x + -9x + 16x2 = 17 + 9x + -17 + -9x Combine like terms: 32x + -9x = 23x -17 + 23x + 16x2 = 17 + 9x + -17 + -9x Reorder the terms: -17 + 23x + 16x2 = 17 + -17 + 9x + -9x Combine like terms: 17 + -17 = 0 -17 + 23x + 16x2 = 0 + 9x + -9x -17 + 23x + 16x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -17 + 23x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.0625 + 1.4375x + x2 = 0 Move the constant term to the right: Add '1.0625' to each side of the equation. -1.0625 + 1.4375x + 1.0625 + x2 = 0 + 1.0625 Reorder the terms: -1.0625 + 1.0625 + 1.4375x + x2 = 0 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + 1.4375x + x2 = 0 + 1.0625 1.4375x + x2 = 0 + 1.0625 Combine like terms: 0 + 1.0625 = 1.0625 1.4375x + x2 = 1.0625 The x term is 1.4375x. Take half its coefficient (0.71875). Square it (0.5166015625) and add it to both sides. Add '0.5166015625' to each side of the equation. 1.4375x + 0.5166015625 + x2 = 1.0625 + 0.5166015625 Reorder the terms: 0.5166015625 + 1.4375x + x2 = 1.0625 + 0.5166015625 Combine like terms: 1.0625 + 0.5166015625 = 1.5791015625 0.5166015625 + 1.4375x + x2 = 1.5791015625 Factor a perfect square on the left side: (x + 0.71875)(x + 0.71875) = 1.5791015625 Calculate the square root of the right side: 1.256623079 Break this problem into two subproblems by setting (x + 0.71875) equal to 1.256623079 and -1.256623079.Subproblem 1
x + 0.71875 = 1.256623079 Simplifying x + 0.71875 = 1.256623079 Reorder the terms: 0.71875 + x = 1.256623079 Solving 0.71875 + x = 1.256623079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + x = 1.256623079 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + x = 1.256623079 + -0.71875 x = 1.256623079 + -0.71875 Combine like terms: 1.256623079 + -0.71875 = 0.537873079 x = 0.537873079 Simplifying x = 0.537873079Subproblem 2
x + 0.71875 = -1.256623079 Simplifying x + 0.71875 = -1.256623079 Reorder the terms: 0.71875 + x = -1.256623079 Solving 0.71875 + x = -1.256623079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.71875' to each side of the equation. 0.71875 + -0.71875 + x = -1.256623079 + -0.71875 Combine like terms: 0.71875 + -0.71875 = 0.00000 0.00000 + x = -1.256623079 + -0.71875 x = -1.256623079 + -0.71875 Combine like terms: -1.256623079 + -0.71875 = -1.975373079 x = -1.975373079 Simplifying x = -1.975373079Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.537873079, -1.975373079}
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