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Simplifying 9x2 + -45x + -4 = 0 Reorder the terms: -4 + -45x + 9x2 = 0 Solving -4 + -45x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -5x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -5x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -5x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -5x + x2 = 0 + 0.4444444444 -5x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -5x + x2 = 0.4444444444 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 0.4444444444 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.4444444444 + 6.25 Combine like terms: 0.4444444444 + 6.25 = 6.6944444444 6.25 + -5x + x2 = 6.6944444444 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.6944444444 Calculate the square root of the right side: 2.587362449 Break this problem into two subproblems by setting (x + -2.5) equal to 2.587362449 and -2.587362449.Subproblem 1
x + -2.5 = 2.587362449 Simplifying x + -2.5 = 2.587362449 Reorder the terms: -2.5 + x = 2.587362449 Solving -2.5 + x = 2.587362449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.587362449 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.587362449 + 2.5 x = 2.587362449 + 2.5 Combine like terms: 2.587362449 + 2.5 = 5.087362449 x = 5.087362449 Simplifying x = 5.087362449Subproblem 2
x + -2.5 = -2.587362449 Simplifying x + -2.5 = -2.587362449 Reorder the terms: -2.5 + x = -2.587362449 Solving -2.5 + x = -2.587362449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.587362449 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.587362449 + 2.5 x = -2.587362449 + 2.5 Combine like terms: -2.587362449 + 2.5 = -0.087362449 x = -0.087362449 Simplifying x = -0.087362449Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.087362449, -0.087362449}
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