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Simplifying 4x2 + -25x + 17 = 9x + 2 Reorder the terms: 17 + -25x + 4x2 = 9x + 2 Reorder the terms: 17 + -25x + 4x2 = 2 + 9x Solving 17 + -25x + 4x2 = 2 + 9x Solving for variable 'x'. Reorder the terms: 17 + -2 + -25x + -9x + 4x2 = 2 + 9x + -2 + -9x Combine like terms: 17 + -2 = 15 15 + -25x + -9x + 4x2 = 2 + 9x + -2 + -9x Combine like terms: -25x + -9x = -34x 15 + -34x + 4x2 = 2 + 9x + -2 + -9x Reorder the terms: 15 + -34x + 4x2 = 2 + -2 + 9x + -9x Combine like terms: 2 + -2 = 0 15 + -34x + 4x2 = 0 + 9x + -9x 15 + -34x + 4x2 = 9x + -9x Combine like terms: 9x + -9x = 0 15 + -34x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -8.5x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -8.5x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -8.5x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -8.5x + x2 = 0 + -3.75 -8.5x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -8.5x + x2 = -3.75 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = -3.75 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -3.75 + 18.0625 Combine like terms: -3.75 + 18.0625 = 14.3125 18.0625 + -8.5x + x2 = 14.3125 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 14.3125 Calculate the square root of the right side: 3.783186488 Break this problem into two subproblems by setting (x + -4.25) equal to 3.783186488 and -3.783186488.Subproblem 1
x + -4.25 = 3.783186488 Simplifying x + -4.25 = 3.783186488 Reorder the terms: -4.25 + x = 3.783186488 Solving -4.25 + x = 3.783186488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 3.783186488 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 3.783186488 + 4.25 x = 3.783186488 + 4.25 Combine like terms: 3.783186488 + 4.25 = 8.033186488 x = 8.033186488 Simplifying x = 8.033186488Subproblem 2
x + -4.25 = -3.783186488 Simplifying x + -4.25 = -3.783186488 Reorder the terms: -4.25 + x = -3.783186488 Solving -4.25 + x = -3.783186488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -3.783186488 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -3.783186488 + 4.25 x = -3.783186488 + 4.25 Combine like terms: -3.783186488 + 4.25 = 0.466813512 x = 0.466813512 Simplifying x = 0.466813512Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.033186488, 0.466813512}
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