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Simplifying (4x + 3)(x + 1) = 2 Reorder the terms: (3 + 4x)(x + 1) = 2 Reorder the terms: (3 + 4x)(1 + x) = 2 Multiply (3 + 4x) * (1 + x) (3(1 + x) + 4x * (1 + x)) = 2 ((1 * 3 + x * 3) + 4x * (1 + x)) = 2 ((3 + 3x) + 4x * (1 + x)) = 2 (3 + 3x + (1 * 4x + x * 4x)) = 2 (3 + 3x + (4x + 4x2)) = 2 Combine like terms: 3x + 4x = 7x (3 + 7x + 4x2) = 2 Solving 3 + 7x + 4x2 = 2 Solving for variable 'x'. Reorder the terms: 3 + -2 + 7x + 4x2 = 2 + -2 Combine like terms: 3 + -2 = 1 1 + 7x + 4x2 = 2 + -2 Combine like terms: 2 + -2 = 0 1 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 1.75x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.75x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.75x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.75x + x2 = 0 + -0.25 1.75x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.75x + x2 = -0.25 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = -0.25 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = -0.25 + 0.765625 Combine like terms: -0.25 + 0.765625 = 0.515625 0.765625 + 1.75x + x2 = 0.515625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (x + 0.875) equal to 0.718070331 and -0.718070331.Subproblem 1
x + 0.875 = 0.718070331 Simplifying x + 0.875 = 0.718070331 Reorder the terms: 0.875 + x = 0.718070331 Solving 0.875 + x = 0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 0.718070331 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 0.718070331 + -0.875 x = 0.718070331 + -0.875 Combine like terms: 0.718070331 + -0.875 = -0.156929669 x = -0.156929669 Simplifying x = -0.156929669Subproblem 2
x + 0.875 = -0.718070331 Simplifying x + 0.875 = -0.718070331 Reorder the terms: 0.875 + x = -0.718070331 Solving 0.875 + x = -0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -0.718070331 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -0.718070331 + -0.875 x = -0.718070331 + -0.875 Combine like terms: -0.718070331 + -0.875 = -1.593070331 x = -1.593070331 Simplifying x = -1.593070331Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.156929669, -1.593070331}
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