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Simplifying 4x(x + -2) = 17 Reorder the terms: 4x(-2 + x) = 17 (-2 * 4x + x * 4x) = 17 (-8x + 4x2) = 17 Solving -8x + 4x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + -8x + 4x2 = 17 + -17 Combine like terms: 17 + -17 = 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 = 3.291287847 x = 3.291287847 Simplifying x = 3.291287847Subproblem 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 = -1.291287847 x = -1.291287847 Simplifying x = -1.291287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.291287847, -1.291287847}
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