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Simplifying 5x(5x + 66) = 180 Reorder the terms: 5x(66 + 5x) = 180 (66 * 5x + 5x * 5x) = 180 (330x + 25x2) = 180 Solving 330x + 25x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 330x + 25x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 330x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-36 + 66x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-36 + 66x + 5x2)' equal to zero and attempt to solve: Simplifying -36 + 66x + 5x2 = 0 Solving -36 + 66x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + 13.2x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 13.2x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 13.2x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 13.2x + x2 = 0 + 7.2 13.2x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 13.2x + x2 = 7.2 The x term is 13.2x. Take half its coefficient (6.6). Square it (43.56) and add it to both sides. Add '43.56' to each side of the equation. 13.2x + 43.56 + x2 = 7.2 + 43.56 Reorder the terms: 43.56 + 13.2x + x2 = 7.2 + 43.56 Combine like terms: 7.2 + 43.56 = 50.76 43.56 + 13.2x + x2 = 50.76 Factor a perfect square on the left side: (x + 6.6)(x + 6.6) = 50.76 Calculate the square root of the right side: 7.124605252 Break this problem into two subproblems by setting (x + 6.6) equal to 7.124605252 and -7.124605252.Subproblem 1
x + 6.6 = 7.124605252 Simplifying x + 6.6 = 7.124605252 Reorder the terms: 6.6 + x = 7.124605252 Solving 6.6 + x = 7.124605252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.6' to each side of the equation. 6.6 + -6.6 + x = 7.124605252 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = 7.124605252 + -6.6 x = 7.124605252 + -6.6 Combine like terms: 7.124605252 + -6.6 = 0.524605252 x = 0.524605252 Simplifying x = 0.524605252Subproblem 2
x + 6.6 = -7.124605252 Simplifying x + 6.6 = -7.124605252 Reorder the terms: 6.6 + x = -7.124605252 Solving 6.6 + x = -7.124605252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.6' to each side of the equation. 6.6 + -6.6 + x = -7.124605252 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = -7.124605252 + -6.6 x = -7.124605252 + -6.6 Combine like terms: -7.124605252 + -6.6 = -13.724605252 x = -13.724605252 Simplifying x = -13.724605252Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.524605252, -13.724605252}Solution
x = {0.524605252, -13.724605252}
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