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Simplifying 2x2 + -18x + -46 = 0 Reorder the terms: -46 + -18x + 2x2 = 0 Solving -46 + -18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-23 + -9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + -9x + x2)' equal to zero and attempt to solve: Simplifying -23 + -9x + x2 = 0 Solving -23 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -9x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -9x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -9x + x2 = 0 + 23 -9x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -9x + x2 = 23 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 = 23 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 23 + 20.25 Combine like terms: 23 + 20.25 = 43.25 20.25 + -9x + x2 = 43.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + -4.5) equal to 6.576473219 and -6.576473219.Subproblem 1
x + -4.5 = 6.576473219 Simplifying x + -4.5 = 6.576473219 Reorder the terms: -4.5 + x = 6.576473219 Solving -4.5 + x = 6.576473219 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 = 6.576473219 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.576473219 + 4.5 x = 6.576473219 + 4.5 Combine like terms: 6.576473219 + 4.5 = 11.076473219 x = 11.076473219 Simplifying x = 11.076473219Subproblem 2
x + -4.5 = -6.576473219 Simplifying x + -4.5 = -6.576473219 Reorder the terms: -4.5 + x = -6.576473219 Solving -4.5 + x = -6.576473219 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 = -6.576473219 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.576473219 + 4.5 x = -6.576473219 + 4.5 Combine like terms: -6.576473219 + 4.5 = -2.076473219 x = -2.076473219 Simplifying x = -2.076473219Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.076473219, -2.076473219}Solution
x = {11.076473219, -2.076473219}
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