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Simplifying 6x2 + -54x = 18 Reorder the terms: -54x + 6x2 = 18 Solving -54x + 6x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + -54x + 6x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -54x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + -9x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + -9x + x2)' equal to zero and attempt to solve: Simplifying -3 + -9x + x2 = 0 Solving -3 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -9x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -9x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -9x + x2 = 0 + 3 -9x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -9x + x2 = 3 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 = 3 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 3 + 20.25 Combine like terms: 3 + 20.25 = 23.25 20.25 + -9x + x2 = 23.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (x + -4.5) equal to 4.82182538 and -4.82182538.Subproblem 1
x + -4.5 = 4.82182538 Simplifying x + -4.5 = 4.82182538 Reorder the terms: -4.5 + x = 4.82182538 Solving -4.5 + x = 4.82182538 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 = 4.82182538 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.82182538 + 4.5 x = 4.82182538 + 4.5 Combine like terms: 4.82182538 + 4.5 = 9.32182538 x = 9.32182538 Simplifying x = 9.32182538Subproblem 2
x + -4.5 = -4.82182538 Simplifying x + -4.5 = -4.82182538 Reorder the terms: -4.5 + x = -4.82182538 Solving -4.5 + x = -4.82182538 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 = -4.82182538 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.82182538 + 4.5 x = -4.82182538 + 4.5 Combine like terms: -4.82182538 + 4.5 = -0.32182538 x = -0.32182538 Simplifying x = -0.32182538Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.32182538, -0.32182538}Solution
x = {9.32182538, -0.32182538}
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