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Simplifying 7x(x + -3) = 4(x + 5) Reorder the terms: 7x(-3 + x) = 4(x + 5) (-3 * 7x + x * 7x) = 4(x + 5) (-21x + 7x2) = 4(x + 5) Reorder the terms: -21x + 7x2 = 4(5 + x) -21x + 7x2 = (5 * 4 + x * 4) -21x + 7x2 = (20 + 4x) Solving -21x + 7x2 = 20 + 4x Solving for variable 'x'. Reorder the terms: -20 + -21x + -4x + 7x2 = 20 + 4x + -20 + -4x Combine like terms: -21x + -4x = -25x -20 + -25x + 7x2 = 20 + 4x + -20 + -4x Reorder the terms: -20 + -25x + 7x2 = 20 + -20 + 4x + -4x Combine like terms: 20 + -20 = 0 -20 + -25x + 7x2 = 0 + 4x + -4x -20 + -25x + 7x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -20 + -25x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.857142857 + -3.571428571x + x2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -3.571428571x + 2.857142857 + x2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -3.571428571x + x2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -3.571428571x + x2 = 0 + 2.857142857 -3.571428571x + x2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -3.571428571x + x2 = 2.857142857 The x term is -3.571428571x. Take half its coefficient (-1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. -3.571428571x + 3.188775511 + x2 = 2.857142857 + 3.188775511 Reorder the terms: 3.188775511 + -3.571428571x + x2 = 2.857142857 + 3.188775511 Combine like terms: 2.857142857 + 3.188775511 = 6.045918368 3.188775511 + -3.571428571x + x2 = 6.045918368 Factor a perfect square on the left side: (x + -1.785714286)(x + -1.785714286) = 6.045918368 Calculate the square root of the right side: 2.458844926 Break this problem into two subproblems by setting (x + -1.785714286) equal to 2.458844926 and -2.458844926.Subproblem 1
x + -1.785714286 = 2.458844926 Simplifying x + -1.785714286 = 2.458844926 Reorder the terms: -1.785714286 + x = 2.458844926 Solving -1.785714286 + x = 2.458844926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = 2.458844926 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = 2.458844926 + 1.785714286 x = 2.458844926 + 1.785714286 Combine like terms: 2.458844926 + 1.785714286 = 4.244559212 x = 4.244559212 Simplifying x = 4.244559212Subproblem 2
x + -1.785714286 = -2.458844926 Simplifying x + -1.785714286 = -2.458844926 Reorder the terms: -1.785714286 + x = -2.458844926 Solving -1.785714286 + x = -2.458844926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = -2.458844926 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = -2.458844926 + 1.785714286 x = -2.458844926 + 1.785714286 Combine like terms: -2.458844926 + 1.785714286 = -0.67313064 x = -0.67313064 Simplifying x = -0.67313064Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.244559212, -0.67313064}
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