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Simplifying (x + -5)(5x + 8) = 8 Reorder the terms: (-5 + x)(5x + 8) = 8 Reorder the terms: (-5 + x)(8 + 5x) = 8 Multiply (-5 + x) * (8 + 5x) (-5(8 + 5x) + x(8 + 5x)) = 8 ((8 * -5 + 5x * -5) + x(8 + 5x)) = 8 ((-40 + -25x) + x(8 + 5x)) = 8 (-40 + -25x + (8 * x + 5x * x)) = 8 (-40 + -25x + (8x + 5x2)) = 8 Combine like terms: -25x + 8x = -17x (-40 + -17x + 5x2) = 8 Solving -40 + -17x + 5x2 = 8 Solving for variable 'x'. Reorder the terms: -40 + -8 + -17x + 5x2 = 8 + -8 Combine like terms: -40 + -8 = -48 -48 + -17x + 5x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -48 + -17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.6 + -3.4x + x2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + -3.4x + 9.6 + x2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + -3.4x + x2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + -3.4x + x2 = 0 + 9.6 -3.4x + x2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 -3.4x + x2 = 9.6 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 9.6 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 9.6 + 2.89 Combine like terms: 9.6 + 2.89 = 12.49 2.89 + -3.4x + x2 = 12.49 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 12.49 Calculate the square root of the right side: 3.534119409 Break this problem into two subproblems by setting (x + -1.7) equal to 3.534119409 and -3.534119409.Subproblem 1
x + -1.7 = 3.534119409 Simplifying x + -1.7 = 3.534119409 Reorder the terms: -1.7 + x = 3.534119409 Solving -1.7 + x = 3.534119409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 3.534119409 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 3.534119409 + 1.7 x = 3.534119409 + 1.7 Combine like terms: 3.534119409 + 1.7 = 5.234119409 x = 5.234119409 Simplifying x = 5.234119409Subproblem 2
x + -1.7 = -3.534119409 Simplifying x + -1.7 = -3.534119409 Reorder the terms: -1.7 + x = -3.534119409 Solving -1.7 + x = -3.534119409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -3.534119409 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -3.534119409 + 1.7 x = -3.534119409 + 1.7 Combine like terms: -3.534119409 + 1.7 = -1.834119409 x = -1.834119409 Simplifying x = -1.834119409Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.234119409, -1.834119409}
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