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Simplifying (7x)(2x + 27) = 180 Remove parenthesis around (7x) 7x(2x + 27) = 180 Reorder the terms: 7x(27 + 2x) = 180 (27 * 7x + 2x * 7x) = 180 (189x + 14x2) = 180 Solving 189x + 14x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 189x + 14x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 189x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -12.85714286 + 13.5x + x2 = 0 Move the constant term to the right: Add '12.85714286' to each side of the equation. -12.85714286 + 13.5x + 12.85714286 + x2 = 0 + 12.85714286 Reorder the terms: -12.85714286 + 12.85714286 + 13.5x + x2 = 0 + 12.85714286 Combine like terms: -12.85714286 + 12.85714286 = 0.00000000 0.00000000 + 13.5x + x2 = 0 + 12.85714286 13.5x + x2 = 0 + 12.85714286 Combine like terms: 0 + 12.85714286 = 12.85714286 13.5x + x2 = 12.85714286 The x term is 13.5x. Take half its coefficient (6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. 13.5x + 45.5625 + x2 = 12.85714286 + 45.5625 Reorder the terms: 45.5625 + 13.5x + x2 = 12.85714286 + 45.5625 Combine like terms: 12.85714286 + 45.5625 = 58.41964286 45.5625 + 13.5x + x2 = 58.41964286 Factor a perfect square on the left side: (x + 6.75)(x + 6.75) = 58.41964286 Calculate the square root of the right side: 7.643274355 Break this problem into two subproblems by setting (x + 6.75) equal to 7.643274355 and -7.643274355.Subproblem 1
x + 6.75 = 7.643274355 Simplifying x + 6.75 = 7.643274355 Reorder the terms: 6.75 + x = 7.643274355 Solving 6.75 + x = 7.643274355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = 7.643274355 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = 7.643274355 + -6.75 x = 7.643274355 + -6.75 Combine like terms: 7.643274355 + -6.75 = 0.893274355 x = 0.893274355 Simplifying x = 0.893274355Subproblem 2
x + 6.75 = -7.643274355 Simplifying x + 6.75 = -7.643274355 Reorder the terms: 6.75 + x = -7.643274355 Solving 6.75 + x = -7.643274355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.75' to each side of the equation. 6.75 + -6.75 + x = -7.643274355 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + x = -7.643274355 + -6.75 x = -7.643274355 + -6.75 Combine like terms: -7.643274355 + -6.75 = -14.393274355 x = -14.393274355 Simplifying x = -14.393274355Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.893274355, -14.393274355}
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