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Simplifying 2x2 + -54 + 30x = 0 Reorder the terms: -54 + 30x + 2x2 = 0 Solving -54 + 30x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + 15x + x2)' equal to zero and attempt to solve: Simplifying -27 + 15x + x2 = 0 Solving -27 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 15x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 15x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 15x + x2 = 0 + 27 15x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 15x + x2 = 27 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 27 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 27 + 56.25 Combine like terms: 27 + 56.25 = 83.25 56.25 + 15x + x2 = 83.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 83.25 Calculate the square root of the right side: 9.124143795 Break this problem into two subproblems by setting (x + 7.5) equal to 9.124143795 and -9.124143795.Subproblem 1
x + 7.5 = 9.124143795 Simplifying x + 7.5 = 9.124143795 Reorder the terms: 7.5 + x = 9.124143795 Solving 7.5 + x = 9.124143795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 9.124143795 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.124143795 + -7.5 x = 9.124143795 + -7.5 Combine like terms: 9.124143795 + -7.5 = 1.624143795 x = 1.624143795 Simplifying x = 1.624143795Subproblem 2
x + 7.5 = -9.124143795 Simplifying x + 7.5 = -9.124143795 Reorder the terms: 7.5 + x = -9.124143795 Solving 7.5 + x = -9.124143795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -9.124143795 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.124143795 + -7.5 x = -9.124143795 + -7.5 Combine like terms: -9.124143795 + -7.5 = -16.624143795 x = -16.624143795 Simplifying x = -16.624143795Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.624143795, -16.624143795}Solution
x = {1.624143795, -16.624143795}
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