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Simplifying 12x2 + -120x + 162 = 0 Reorder the terms: 162 + -120x + 12x2 = 0 Solving 162 + -120x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(27 + -20x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(27 + -20x + 2x2)' equal to zero and attempt to solve: Simplifying 27 + -20x + 2x2 = 0 Solving 27 + -20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + -10x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -10x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -10x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -10x + x2 = 0 + -13.5 -10x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -10x + x2 = -13.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -13.5 + 25 Reorder the terms: 25 + -10x + x2 = -13.5 + 25 Combine like terms: -13.5 + 25 = 11.5 25 + -10x + x2 = 11.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + -5) equal to 3.391164992 and -3.391164992.Subproblem 1
x + -5 = 3.391164992 Simplifying x + -5 = 3.391164992 Reorder the terms: -5 + x = 3.391164992 Solving -5 + x = 3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.391164992 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.391164992 + 5 x = 3.391164992 + 5 Combine like terms: 3.391164992 + 5 = 8.391164992 x = 8.391164992 Simplifying x = 8.391164992Subproblem 2
x + -5 = -3.391164992 Simplifying x + -5 = -3.391164992 Reorder the terms: -5 + x = -3.391164992 Solving -5 + x = -3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.391164992 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.391164992 + 5 x = -3.391164992 + 5 Combine like terms: -3.391164992 + 5 = 1.608835008 x = 1.608835008 Simplifying x = 1.608835008Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.391164992, 1.608835008}Solution
x = {8.391164992, 1.608835008}
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