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Simplifying 6x2 + 54x = 9 Reorder the terms: 54x + 6x2 = 9 Solving 54x + 6x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 54x + 6x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 54x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 18x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 18x + 2x2)' equal to zero and attempt to solve: Simplifying -3 + 18x + 2x2 = 0 Solving -3 + 18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 9x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 9x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 9x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 9x + x2 = 0 + 1.5 9x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 9x + x2 = 1.5 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 = 1.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 1.5 + 20.25 Combine like terms: 1.5 + 20.25 = 21.75 20.25 + 9x + x2 = 21.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 21.75 Calculate the square root of the right side: 4.663689527 Break this problem into two subproblems by setting (x + 4.5) equal to 4.663689527 and -4.663689527.Subproblem 1
x + 4.5 = 4.663689527 Simplifying x + 4.5 = 4.663689527 Reorder the terms: 4.5 + x = 4.663689527 Solving 4.5 + x = 4.663689527 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 = 4.663689527 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.663689527 + -4.5 x = 4.663689527 + -4.5 Combine like terms: 4.663689527 + -4.5 = 0.163689527 x = 0.163689527 Simplifying x = 0.163689527Subproblem 2
x + 4.5 = -4.663689527 Simplifying x + 4.5 = -4.663689527 Reorder the terms: 4.5 + x = -4.663689527 Solving 4.5 + x = -4.663689527 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 = -4.663689527 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.663689527 + -4.5 x = -4.663689527 + -4.5 Combine like terms: -4.663689527 + -4.5 = -9.163689527 x = -9.163689527 Simplifying x = -9.163689527Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.163689527, -9.163689527}Solution
x = {0.163689527, -9.163689527}
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