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Simplifying (5x + 15)(x + -8) = 46 Reorder the terms: (15 + 5x)(x + -8) = 46 Reorder the terms: (15 + 5x)(-8 + x) = 46 Multiply (15 + 5x) * (-8 + x) (15(-8 + x) + 5x * (-8 + x)) = 46 ((-8 * 15 + x * 15) + 5x * (-8 + x)) = 46 ((-120 + 15x) + 5x * (-8 + x)) = 46 (-120 + 15x + (-8 * 5x + x * 5x)) = 46 (-120 + 15x + (-40x + 5x2)) = 46 Combine like terms: 15x + -40x = -25x (-120 + -25x + 5x2) = 46 Solving -120 + -25x + 5x2 = 46 Solving for variable 'x'. Reorder the terms: -120 + -46 + -25x + 5x2 = 46 + -46 Combine like terms: -120 + -46 = -166 -166 + -25x + 5x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -166 + -25x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -33.2 + -5x + x2 = 0 Move the constant term to the right: Add '33.2' to each side of the equation. -33.2 + -5x + 33.2 + x2 = 0 + 33.2 Reorder the terms: -33.2 + 33.2 + -5x + x2 = 0 + 33.2 Combine like terms: -33.2 + 33.2 = 0.0 0.0 + -5x + x2 = 0 + 33.2 -5x + x2 = 0 + 33.2 Combine like terms: 0 + 33.2 = 33.2 -5x + x2 = 33.2 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 33.2 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 33.2 + 6.25 Combine like terms: 33.2 + 6.25 = 39.45 6.25 + -5x + x2 = 39.45 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 39.45 Calculate the square root of the right side: 6.280923499 Break this problem into two subproblems by setting (x + -2.5) equal to 6.280923499 and -6.280923499.Subproblem 1
x + -2.5 = 6.280923499 Simplifying x + -2.5 = 6.280923499 Reorder the terms: -2.5 + x = 6.280923499 Solving -2.5 + x = 6.280923499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 6.280923499 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.280923499 + 2.5 x = 6.280923499 + 2.5 Combine like terms: 6.280923499 + 2.5 = 8.780923499 x = 8.780923499 Simplifying x = 8.780923499Subproblem 2
x + -2.5 = -6.280923499 Simplifying x + -2.5 = -6.280923499 Reorder the terms: -2.5 + x = -6.280923499 Solving -2.5 + x = -6.280923499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -6.280923499 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.280923499 + 2.5 x = -6.280923499 + 2.5 Combine like terms: -6.280923499 + 2.5 = -3.780923499 x = -3.780923499 Simplifying x = -3.780923499Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.780923499, -3.780923499}
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