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Simplifying 4 + 2x + -1x2 = 11x Solving 4 + 2x + -1x2 = 11x Solving for variable 'x'. Reorder the terms: 4 + 2x + -11x + -1x2 = 11x + -11x Combine like terms: 2x + -11x = -9x 4 + -9x + -1x2 = 11x + -11x Combine like terms: 11x + -11x = 0 4 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 9x + x2 = 0 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 = 0.424428901 x = 0.424428901 Simplifying x = 0.424428901Subproblem 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 = -9.424428901 x = -9.424428901 Simplifying x = -9.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.424428901, -9.424428901}
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