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Simplifying (5x)(2x + 5) = 180 Remove parenthesis around (5x) 5x(2x + 5) = 180 Reorder the terms: 5x(5 + 2x) = 180 (5 * 5x + 2x * 5x) = 180 (25x + 10x2) = 180 Solving 25x + 10x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 25x + 10x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 25x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-36 + 5x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-36 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying -36 + 5x + 2x2 = 0 Solving -36 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18 + 2.5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 2.5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 2.5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 2.5x + x2 = 0 + 18 2.5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 2.5x + x2 = 18 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 18 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 18 + 1.5625 Combine like terms: 18 + 1.5625 = 19.5625 1.5625 + 2.5x + x2 = 19.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 19.5625 Calculate the square root of the right side: 4.422951503 Break this problem into two subproblems by setting (x + 1.25) equal to 4.422951503 and -4.422951503.Subproblem 1
x + 1.25 = 4.422951503 Simplifying x + 1.25 = 4.422951503 Reorder the terms: 1.25 + x = 4.422951503 Solving 1.25 + x = 4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 4.422951503 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 4.422951503 + -1.25 x = 4.422951503 + -1.25 Combine like terms: 4.422951503 + -1.25 = 3.172951503 x = 3.172951503 Simplifying x = 3.172951503Subproblem 2
x + 1.25 = -4.422951503 Simplifying x + 1.25 = -4.422951503 Reorder the terms: 1.25 + x = -4.422951503 Solving 1.25 + x = -4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -4.422951503 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -4.422951503 + -1.25 x = -4.422951503 + -1.25 Combine like terms: -4.422951503 + -1.25 = -5.672951503 x = -5.672951503 Simplifying x = -5.672951503Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.172951503, -5.672951503}Solution
x = {3.172951503, -5.672951503}
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