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Simplifying 6x2 = 54x + 36 + 0 Reorder the terms: 6x2 = 36 + 0 + 54x Combine like terms: 36 + 0 = 36 6x2 = 36 + 54x Solving 6x2 = 36 + 54x Solving for variable 'x'. Reorder the terms: -36 + -54x + 6x2 = 36 + 54x + -36 + -54x Reorder the terms: -36 + -54x + 6x2 = 36 + -36 + 54x + -54x Combine like terms: 36 + -36 = 0 -36 + -54x + 6x2 = 0 + 54x + -54x -36 + -54x + 6x2 = 54x + -54x Combine like terms: 54x + -54x = 0 -36 + -54x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-6 + -9x + x2) = 0 Ignore the factor 6.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 = 26.25 20.25 + -9x + x2 = 26.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + -4.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + -4.5 = 5.123475383 Simplifying x + -4.5 = 5.123475383 Reorder the terms: -4.5 + x = 5.123475383 Solving -4.5 + x = 5.123475383 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 = 5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.123475383 + 4.5 x = 5.123475383 + 4.5 Combine like terms: 5.123475383 + 4.5 = 9.623475383 x = 9.623475383 Simplifying x = 9.623475383Subproblem 2
x + -4.5 = -5.123475383 Simplifying x + -4.5 = -5.123475383 Reorder the terms: -4.5 + x = -5.123475383 Solving -4.5 + x = -5.123475383 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 = -5.123475383 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.123475383 + 4.5 x = -5.123475383 + 4.5 Combine like terms: -5.123475383 + 4.5 = -0.623475383 x = -0.623475383 Simplifying x = -0.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.623475383, -0.623475383}Solution
x = {9.623475383, -0.623475383}
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