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Simplifying x(x + 1) = 10x + 4 Reorder the terms: x(1 + x) = 10x + 4 (1 * x + x * x) = 10x + 4 (1x + x2) = 10x + 4 Reorder the terms: 1x + x2 = 4 + 10x Solving 1x + x2 = 4 + 10x Solving for variable 'x'. Reorder the terms: -4 + 1x + -10x + x2 = 4 + 10x + -4 + -10x Combine like terms: 1x + -10x = -9x -4 + -9x + x2 = 4 + 10x + -4 + -10x Reorder the terms: -4 + -9x + x2 = 4 + -4 + 10x + -10x Combine like terms: 4 + -4 = 0 -4 + -9x + x2 = 0 + 10x + -10x -4 + -9x + x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -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}
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