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Simplifying (5x + 30)(5x + 30) = 90 Reorder the terms: (30 + 5x)(5x + 30) = 90 Reorder the terms: (30 + 5x)(30 + 5x) = 90 Multiply (30 + 5x) * (30 + 5x) (30(30 + 5x) + 5x * (30 + 5x)) = 90 ((30 * 30 + 5x * 30) + 5x * (30 + 5x)) = 90 ((900 + 150x) + 5x * (30 + 5x)) = 90 (900 + 150x + (30 * 5x + 5x * 5x)) = 90 (900 + 150x + (150x + 25x2)) = 90 Combine like terms: 150x + 150x = 300x (900 + 300x + 25x2) = 90 Solving 900 + 300x + 25x2 = 90 Solving for variable 'x'. Reorder the terms: 900 + -90 + 300x + 25x2 = 90 + -90 Combine like terms: 900 + -90 = 810 810 + 300x + 25x2 = 90 + -90 Combine like terms: 90 + -90 = 0 810 + 300x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(162 + 60x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(162 + 60x + 5x2)' equal to zero and attempt to solve: Simplifying 162 + 60x + 5x2 = 0 Solving 162 + 60x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 32.4 + 12x + x2 = 0 Move the constant term to the right: Add '-32.4' to each side of the equation. 32.4 + 12x + -32.4 + x2 = 0 + -32.4 Reorder the terms: 32.4 + -32.4 + 12x + x2 = 0 + -32.4 Combine like terms: 32.4 + -32.4 = 0.0 0.0 + 12x + x2 = 0 + -32.4 12x + x2 = 0 + -32.4 Combine like terms: 0 + -32.4 = -32.4 12x + x2 = -32.4 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -32.4 + 36 Reorder the terms: 36 + 12x + x2 = -32.4 + 36 Combine like terms: -32.4 + 36 = 3.6 36 + 12x + x2 = 3.6 Factor a perfect square on the left side: (x + 6)(x + 6) = 3.6 Calculate the square root of the right side: 1.897366596 Break this problem into two subproblems by setting (x + 6) equal to 1.897366596 and -1.897366596.Subproblem 1
x + 6 = 1.897366596 Simplifying x + 6 = 1.897366596 Reorder the terms: 6 + x = 1.897366596 Solving 6 + x = 1.897366596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 1.897366596 + -6 Combine like terms: 6 + -6 = 0 0 + x = 1.897366596 + -6 x = 1.897366596 + -6 Combine like terms: 1.897366596 + -6 = -4.102633404 x = -4.102633404 Simplifying x = -4.102633404Subproblem 2
x + 6 = -1.897366596 Simplifying x + 6 = -1.897366596 Reorder the terms: 6 + x = -1.897366596 Solving 6 + x = -1.897366596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -1.897366596 + -6 Combine like terms: 6 + -6 = 0 0 + x = -1.897366596 + -6 x = -1.897366596 + -6 Combine like terms: -1.897366596 + -6 = -7.897366596 x = -7.897366596 Simplifying x = -7.897366596Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.102633404, -7.897366596}Solution
x = {-4.102633404, -7.897366596}
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