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Simplifying 3(x + 1) + 1 + 2x = 2(2x + 2) * x Reorder the terms: 3(1 + x) + 1 + 2x = 2(2x + 2) * x (1 * 3 + x * 3) + 1 + 2x = 2(2x + 2) * x (3 + 3x) + 1 + 2x = 2(2x + 2) * x Reorder the terms: 3 + 1 + 3x + 2x = 2(2x + 2) * x Combine like terms: 3 + 1 = 4 4 + 3x + 2x = 2(2x + 2) * x Combine like terms: 3x + 2x = 5x 4 + 5x = 2(2x + 2) * x Reorder the terms: 4 + 5x = 2(2 + 2x) * x Reorder the terms for easier multiplication: 4 + 5x = 2x(2 + 2x) 4 + 5x = (2 * 2x + 2x * 2x) 4 + 5x = (4x + 4x2) Solving 4 + 5x = 4x + 4x2 Solving for variable 'x'. Combine like terms: 5x + -4x = 1x 4 + 1x + -4x2 = 4x + 4x2 + -4x + -4x2 Reorder the terms: 4 + 1x + -4x2 = 4x + -4x + 4x2 + -4x2 Combine like terms: 4x + -4x = 0 4 + 1x + -4x2 = 0 + 4x2 + -4x2 4 + 1x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 4 + 1x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1 + -0.25x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.25x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.25x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.25x + x2 = 0 + 1 -0.25x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.25x + x2 = 1 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 1 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 1 + 0.015625 Combine like terms: 1 + 0.015625 = 1.015625 0.015625 + -0.25x + x2 = 1.015625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (x + -0.125) equal to 1.007782219 and -1.007782219.Subproblem 1
x + -0.125 = 1.007782219 Simplifying x + -0.125 = 1.007782219 Reorder the terms: -0.125 + x = 1.007782219 Solving -0.125 + x = 1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.007782219 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.007782219 + 0.125 x = 1.007782219 + 0.125 Combine like terms: 1.007782219 + 0.125 = 1.132782219 x = 1.132782219 Simplifying x = 1.132782219Subproblem 2
x + -0.125 = -1.007782219 Simplifying x + -0.125 = -1.007782219 Reorder the terms: -0.125 + x = -1.007782219 Solving -0.125 + x = -1.007782219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.007782219 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.007782219 + 0.125 x = -1.007782219 + 0.125 Combine like terms: -1.007782219 + 0.125 = -0.882782219 x = -0.882782219 Simplifying x = -0.882782219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.132782219, -0.882782219}
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