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Simplifying (4x + 5)(x + -3) = 720 Reorder the terms: (5 + 4x)(x + -3) = 720 Reorder the terms: (5 + 4x)(-3 + x) = 720 Multiply (5 + 4x) * (-3 + x) (5(-3 + x) + 4x * (-3 + x)) = 720 ((-3 * 5 + x * 5) + 4x * (-3 + x)) = 720 ((-15 + 5x) + 4x * (-3 + x)) = 720 (-15 + 5x + (-3 * 4x + x * 4x)) = 720 (-15 + 5x + (-12x + 4x2)) = 720 Combine like terms: 5x + -12x = -7x (-15 + -7x + 4x2) = 720 Solving -15 + -7x + 4x2 = 720 Solving for variable 'x'. Reorder the terms: -15 + -720 + -7x + 4x2 = 720 + -720 Combine like terms: -15 + -720 = -735 -735 + -7x + 4x2 = 720 + -720 Combine like terms: 720 + -720 = 0 -735 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -183.75 + -1.75x + x2 = 0 Move the constant term to the right: Add '183.75' to each side of the equation. -183.75 + -1.75x + 183.75 + x2 = 0 + 183.75 Reorder the terms: -183.75 + 183.75 + -1.75x + x2 = 0 + 183.75 Combine like terms: -183.75 + 183.75 = 0.00 0.00 + -1.75x + x2 = 0 + 183.75 -1.75x + x2 = 0 + 183.75 Combine like terms: 0 + 183.75 = 183.75 -1.75x + x2 = 183.75 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 183.75 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 183.75 + 0.765625 Combine like terms: 183.75 + 0.765625 = 184.515625 0.765625 + -1.75x + x2 = 184.515625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 184.515625 Calculate the square root of the right side: 13.583652859 Break this problem into two subproblems by setting (x + -0.875) equal to 13.583652859 and -13.583652859.Subproblem 1
x + -0.875 = 13.583652859 Simplifying x + -0.875 = 13.583652859 Reorder the terms: -0.875 + x = 13.583652859 Solving -0.875 + x = 13.583652859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 13.583652859 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 13.583652859 + 0.875 x = 13.583652859 + 0.875 Combine like terms: 13.583652859 + 0.875 = 14.458652859 x = 14.458652859 Simplifying x = 14.458652859Subproblem 2
x + -0.875 = -13.583652859 Simplifying x + -0.875 = -13.583652859 Reorder the terms: -0.875 + x = -13.583652859 Solving -0.875 + x = -13.583652859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -13.583652859 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -13.583652859 + 0.875 x = -13.583652859 + 0.875 Combine like terms: -13.583652859 + 0.875 = -12.708652859 x = -12.708652859 Simplifying x = -12.708652859Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.458652859, -12.708652859}
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