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Simplifying 4x2 = -8x + 17 Reorder the terms: 4x2 = 17 + -8x Solving 4x2 = 17 + -8x Solving for variable 'x'. Reorder the terms: -17 + 8x + 4x2 = 17 + -8x + -17 + 8x Reorder the terms: -17 + 8x + 4x2 = 17 + -17 + -8x + 8x Combine like terms: 17 + -17 = 0 -17 + 8x + 4x2 = 0 + -8x + 8x -17 + 8x + 4x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -17 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + 2x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + 2x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + 2x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + 2x + x2 = 0 + 4.25 2x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 2x + x2 = 4.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 4.25 + 1 Reorder the terms: 1 + 2x + x2 = 4.25 + 1 Combine like terms: 4.25 + 1 = 5.25 1 + 2x + x2 = 5.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 1) equal to 2.291287847 and -2.291287847.Subproblem 1
x + 1 = 2.291287847 Simplifying x + 1 = 2.291287847 Reorder the terms: 1 + x = 2.291287847 Solving 1 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.291287847 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.291287847 + -1 x = 2.291287847 + -1 Combine like terms: 2.291287847 + -1 = 1.291287847 x = 1.291287847 Simplifying x = 1.291287847Subproblem 2
x + 1 = -2.291287847 Simplifying x + 1 = -2.291287847 Reorder the terms: 1 + x = -2.291287847 Solving 1 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.291287847 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.291287847 + -1 x = -2.291287847 + -1 Combine like terms: -2.291287847 + -1 = -3.291287847 x = -3.291287847 Simplifying x = -3.291287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.291287847, -3.291287847}
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