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Simplifying x(4 + x) + 3(x + 1) = 0 (4 * x + x * x) + 3(x + 1) = 0 (4x + x2) + 3(x + 1) = 0 Reorder the terms: 4x + x2 + 3(1 + x) = 0 4x + x2 + (1 * 3 + x * 3) = 0 4x + x2 + (3 + 3x) = 0 Reorder the terms: 3 + 4x + 3x + x2 = 0 Combine like terms: 4x + 3x = 7x 3 + 7x + x2 = 0 Solving 3 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 7x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 7x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7x + x2 = 0 + -3 7x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 7x + x2 = -3 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -3 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -3 + 12.25 Combine like terms: -3 + 12.25 = 9.25 12.25 + 7x + x2 = 9.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + 3.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + 3.5 = 3.041381265 Simplifying x + 3.5 = 3.041381265 Reorder the terms: 3.5 + x = 3.041381265 Solving 3.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.041381265 + -3.5 x = 3.041381265 + -3.5 Combine like terms: 3.041381265 + -3.5 = -0.458618735 x = -0.458618735 Simplifying x = -0.458618735Subproblem 2
x + 3.5 = -3.041381265 Simplifying x + 3.5 = -3.041381265 Reorder the terms: 3.5 + x = -3.041381265 Solving 3.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.041381265 + -3.5 x = -3.041381265 + -3.5 Combine like terms: -3.041381265 + -3.5 = -6.541381265 x = -6.541381265 Simplifying x = -6.541381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.458618735, -6.541381265}
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