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Simplifying (4x + -7)(9x + 5) = (8x + -3)(4x + 7) Reorder the terms: (-7 + 4x)(9x + 5) = (8x + -3)(4x + 7) Reorder the terms: (-7 + 4x)(5 + 9x) = (8x + -3)(4x + 7) Multiply (-7 + 4x) * (5 + 9x) (-7(5 + 9x) + 4x * (5 + 9x)) = (8x + -3)(4x + 7) ((5 * -7 + 9x * -7) + 4x * (5 + 9x)) = (8x + -3)(4x + 7) ((-35 + -63x) + 4x * (5 + 9x)) = (8x + -3)(4x + 7) (-35 + -63x + (5 * 4x + 9x * 4x)) = (8x + -3)(4x + 7) (-35 + -63x + (20x + 36x2)) = (8x + -3)(4x + 7) Combine like terms: -63x + 20x = -43x (-35 + -43x + 36x2) = (8x + -3)(4x + 7) Reorder the terms: -35 + -43x + 36x2 = (-3 + 8x)(4x + 7) Reorder the terms: -35 + -43x + 36x2 = (-3 + 8x)(7 + 4x) Multiply (-3 + 8x) * (7 + 4x) -35 + -43x + 36x2 = (-3(7 + 4x) + 8x * (7 + 4x)) -35 + -43x + 36x2 = ((7 * -3 + 4x * -3) + 8x * (7 + 4x)) -35 + -43x + 36x2 = ((-21 + -12x) + 8x * (7 + 4x)) -35 + -43x + 36x2 = (-21 + -12x + (7 * 8x + 4x * 8x)) -35 + -43x + 36x2 = (-21 + -12x + (56x + 32x2)) Combine like terms: -12x + 56x = 44x -35 + -43x + 36x2 = (-21 + 44x + 32x2) Solving -35 + -43x + 36x2 = -21 + 44x + 32x2 Solving for variable 'x'. Reorder the terms: -35 + 21 + -43x + -44x + 36x2 + -32x2 = -21 + 44x + 32x2 + 21 + -44x + -32x2 Combine like terms: -35 + 21 = -14 -14 + -43x + -44x + 36x2 + -32x2 = -21 + 44x + 32x2 + 21 + -44x + -32x2 Combine like terms: -43x + -44x = -87x -14 + -87x + 36x2 + -32x2 = -21 + 44x + 32x2 + 21 + -44x + -32x2 Combine like terms: 36x2 + -32x2 = 4x2 -14 + -87x + 4x2 = -21 + 44x + 32x2 + 21 + -44x + -32x2 Reorder the terms: -14 + -87x + 4x2 = -21 + 21 + 44x + -44x + 32x2 + -32x2 Combine like terms: -21 + 21 = 0 -14 + -87x + 4x2 = 0 + 44x + -44x + 32x2 + -32x2 -14 + -87x + 4x2 = 44x + -44x + 32x2 + -32x2 Combine like terms: 44x + -44x = 0 -14 + -87x + 4x2 = 0 + 32x2 + -32x2 -14 + -87x + 4x2 = 32x2 + -32x2 Combine like terms: 32x2 + -32x2 = 0 -14 + -87x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.5 + -21.75x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -21.75x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -21.75x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -21.75x + x2 = 0 + 3.5 -21.75x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -21.75x + x2 = 3.5 The x term is -21.75x. Take half its coefficient (-10.875). Square it (118.265625) and add it to both sides. Add '118.265625' to each side of the equation. -21.75x + 118.265625 + x2 = 3.5 + 118.265625 Reorder the terms: 118.265625 + -21.75x + x2 = 3.5 + 118.265625 Combine like terms: 3.5 + 118.265625 = 121.765625 118.265625 + -21.75x + x2 = 121.765625 Factor a perfect square on the left side: (x + -10.875)(x + -10.875) = 121.765625 Calculate the square root of the right side: 11.034746259 Break this problem into two subproblems by setting (x + -10.875) equal to 11.034746259 and -11.034746259.Subproblem 1
x + -10.875 = 11.034746259 Simplifying x + -10.875 = 11.034746259 Reorder the terms: -10.875 + x = 11.034746259 Solving -10.875 + x = 11.034746259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.875' to each side of the equation. -10.875 + 10.875 + x = 11.034746259 + 10.875 Combine like terms: -10.875 + 10.875 = 0.000 0.000 + x = 11.034746259 + 10.875 x = 11.034746259 + 10.875 Combine like terms: 11.034746259 + 10.875 = 21.909746259 x = 21.909746259 Simplifying x = 21.909746259Subproblem 2
x + -10.875 = -11.034746259 Simplifying x + -10.875 = -11.034746259 Reorder the terms: -10.875 + x = -11.034746259 Solving -10.875 + x = -11.034746259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.875' to each side of the equation. -10.875 + 10.875 + x = -11.034746259 + 10.875 Combine like terms: -10.875 + 10.875 = 0.000 0.000 + x = -11.034746259 + 10.875 x = -11.034746259 + 10.875 Combine like terms: -11.034746259 + 10.875 = -0.159746259 x = -0.159746259 Simplifying x = -0.159746259Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.909746259, -0.159746259}
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