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Simplifying 2x2 + -18x + -8 = 0 Reorder the terms: -8 + -18x + 2x2 = 0 Solving -8 + -18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -9x + x2)' equal to zero and attempt to solve: Simplifying -4 + -9x + x2 = 0 Solving -4 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -9x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -9x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -9x + x2 = 0 + 4 -9x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -9x + x2 = 4 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 = 4 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 4 + 20.25 Combine like terms: 4 + 20.25 = 24.25 20.25 + -9x + x2 = 24.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + -4.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + -4.5 = 4.924428901 Simplifying x + -4.5 = 4.924428901 Reorder the terms: -4.5 + x = 4.924428901 Solving -4.5 + x = 4.924428901 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 = 4.924428901 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.924428901 + 4.5 x = 4.924428901 + 4.5 Combine like terms: 4.924428901 + 4.5 = 9.424428901 x = 9.424428901 Simplifying x = 9.424428901Subproblem 2
x + -4.5 = -4.924428901 Simplifying x + -4.5 = -4.924428901 Reorder the terms: -4.5 + x = -4.924428901 Solving -4.5 + x = -4.924428901 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 = -4.924428901 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.924428901 + 4.5 x = -4.924428901 + 4.5 Combine like terms: -4.924428901 + 4.5 = -0.424428901 x = -0.424428901 Simplifying x = -0.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.424428901, -0.424428901}Solution
x = {9.424428901, -0.424428901}
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