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Simplifying (4x)(5x + -27) = 180 Remove parenthesis around (4x) 4x(5x + -27) = 180 Reorder the terms: 4x(-27 + 5x) = 180 (-27 * 4x + 5x * 4x) = 180 (-108x + 20x2) = 180 Solving -108x + 20x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -108x + 20x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -108x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + -27x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + -27x + 5x2)' equal to zero and attempt to solve: Simplifying -45 + -27x + 5x2 = 0 Solving -45 + -27x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9 + -5.4x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -5.4x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -5.4x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5.4x + x2 = 0 + 9 -5.4x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -5.4x + x2 = 9 The x term is -5.4x. Take half its coefficient (-2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. -5.4x + 7.29 + x2 = 9 + 7.29 Reorder the terms: 7.29 + -5.4x + x2 = 9 + 7.29 Combine like terms: 9 + 7.29 = 16.29 7.29 + -5.4x + x2 = 16.29 Factor a perfect square on the left side: (x + -2.7)(x + -2.7) = 16.29 Calculate the square root of the right side: 4.036087214 Break this problem into two subproblems by setting (x + -2.7) equal to 4.036087214 and -4.036087214.Subproblem 1
x + -2.7 = 4.036087214 Simplifying x + -2.7 = 4.036087214 Reorder the terms: -2.7 + x = 4.036087214 Solving -2.7 + x = 4.036087214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + x = 4.036087214 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = 4.036087214 + 2.7 x = 4.036087214 + 2.7 Combine like terms: 4.036087214 + 2.7 = 6.736087214 x = 6.736087214 Simplifying x = 6.736087214Subproblem 2
x + -2.7 = -4.036087214 Simplifying x + -2.7 = -4.036087214 Reorder the terms: -2.7 + x = -4.036087214 Solving -2.7 + x = -4.036087214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + x = -4.036087214 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = -4.036087214 + 2.7 x = -4.036087214 + 2.7 Combine like terms: -4.036087214 + 2.7 = -1.336087214 x = -1.336087214 Simplifying x = -1.336087214Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.736087214, -1.336087214}Solution
x = {6.736087214, -1.336087214}
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