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Simplifying 6x2 + -42x + -54 = 0 Reorder the terms: -54 + -42x + 6x2 = 0 Solving -54 + -42x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-9 + -7x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + -7x + x2)' equal to zero and attempt to solve: Simplifying -9 + -7x + x2 = 0 Solving -9 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -7x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -7x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -7x + x2 = 0 + 9 -7x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -7x + x2 = 9 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 9 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 9 + 12.25 Combine like terms: 9 + 12.25 = 21.25 12.25 + -7x + x2 = 21.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + -3.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + -3.5 = 4.609772229 Simplifying x + -3.5 = 4.609772229 Reorder the terms: -3.5 + x = 4.609772229 Solving -3.5 + x = 4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.609772229 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.609772229 + 3.5 x = 4.609772229 + 3.5 Combine like terms: 4.609772229 + 3.5 = 8.109772229 x = 8.109772229 Simplifying x = 8.109772229Subproblem 2
x + -3.5 = -4.609772229 Simplifying x + -3.5 = -4.609772229 Reorder the terms: -3.5 + x = -4.609772229 Solving -3.5 + x = -4.609772229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.609772229 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.609772229 + 3.5 x = -4.609772229 + 3.5 Combine like terms: -4.609772229 + 3.5 = -1.109772229 x = -1.109772229 Simplifying x = -1.109772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.109772229, -1.109772229}Solution
x = {8.109772229, -1.109772229}
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