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Simplifying 5x2 + 45x + 30 = 0 Reorder the terms: 30 + 45x + 5x2 = 0 Solving 30 + 45x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(6 + 9x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + 9x + x2)' equal to zero and attempt to solve: Simplifying 6 + 9x + x2 = 0 Solving 6 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 9x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 9x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 9x + x2 = 0 + -6 9x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 9x + x2 = -6 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -6 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -6 + 20.25 Combine like terms: -6 + 20.25 = 14.25 20.25 + 9x + x2 = 14.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + 4.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + 4.5 = 3.774917218 Simplifying x + 4.5 = 3.774917218 Reorder the terms: 4.5 + x = 3.774917218 Solving 4.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 3.774917218 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 3.774917218 + -4.5 x = 3.774917218 + -4.5 Combine like terms: 3.774917218 + -4.5 = -0.725082782 x = -0.725082782 Simplifying x = -0.725082782Subproblem 2
x + 4.5 = -3.774917218 Simplifying x + 4.5 = -3.774917218 Reorder the terms: 4.5 + x = -3.774917218 Solving 4.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -3.774917218 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -3.774917218 + -4.5 x = -3.774917218 + -4.5 Combine like terms: -3.774917218 + -4.5 = -8.274917218 x = -8.274917218 Simplifying x = -8.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.725082782, -8.274917218}Solution
x = {-0.725082782, -8.274917218}
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