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Simplifying 3x + x2 = 22 Solving 3x + x2 = 22 Solving for variable 'x'. Reorder the terms: -22 + 3x + x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -22 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 3x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 3x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 3x + x2 = 0 + 22 3x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 3x + x2 = 22 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 22 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 22 + 2.25 Combine like terms: 22 + 2.25 = 24.25 2.25 + 3x + x2 = 24.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + 1.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + 1.5 = 4.924428901 Simplifying x + 1.5 = 4.924428901 Reorder the terms: 1.5 + x = 4.924428901 Solving 1.5 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.924428901 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.924428901 + -1.5 x = 4.924428901 + -1.5 Combine like terms: 4.924428901 + -1.5 = 3.424428901 x = 3.424428901 Simplifying x = 3.424428901Subproblem 2
x + 1.5 = -4.924428901 Simplifying x + 1.5 = -4.924428901 Reorder the terms: 1.5 + x = -4.924428901 Solving 1.5 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.924428901 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.924428901 + -1.5 x = -4.924428901 + -1.5 Combine like terms: -4.924428901 + -1.5 = -6.424428901 x = -6.424428901 Simplifying x = -6.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.424428901, -6.424428901}
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