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Simplifying (x + 1.77)(2x + 4) = 0 Reorder the terms: (1.77 + x)(2x + 4) = 0 Reorder the terms: (1.77 + x)(4 + 2x) = 0 Multiply (1.77 + x) * (4 + 2x) (1.77(4 + 2x) + x(4 + 2x)) = 0 ((4 * 1.77 + 2x * 1.77) + x(4 + 2x)) = 0 ((7.08 + 3.54x) + x(4 + 2x)) = 0 (7.08 + 3.54x + (4 * x + 2x * x)) = 0 (7.08 + 3.54x + (4x + 2x2)) = 0 Combine like terms: 3.54x + 4x = 7.54x (7.08 + 7.54x + 2x2) = 0 Solving 7.08 + 7.54x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.54 + 3.77x + x2 = 0 Move the constant term to the right: Add '-3.54' to each side of the equation. 3.54 + 3.77x + -3.54 + x2 = 0 + -3.54 Reorder the terms: 3.54 + -3.54 + 3.77x + x2 = 0 + -3.54 Combine like terms: 3.54 + -3.54 = 0.00 0.00 + 3.77x + x2 = 0 + -3.54 3.77x + x2 = 0 + -3.54 Combine like terms: 0 + -3.54 = -3.54 3.77x + x2 = -3.54 The x term is 3.77x. Take half its coefficient (1.885). Square it (3.553225) and add it to both sides. Add '3.553225' to each side of the equation. 3.77x + 3.553225 + x2 = -3.54 + 3.553225 Reorder the terms: 3.553225 + 3.77x + x2 = -3.54 + 3.553225 Combine like terms: -3.54 + 3.553225 = 0.013225 3.553225 + 3.77x + x2 = 0.013225 Factor a perfect square on the left side: (x + 1.885)(x + 1.885) = 0.013225 Calculate the square root of the right side: 0.115 Break this problem into two subproblems by setting (x + 1.885) equal to 0.115 and -0.115.Subproblem 1
x + 1.885 = 0.115 Simplifying x + 1.885 = 0.115 Reorder the terms: 1.885 + x = 0.115 Solving 1.885 + x = 0.115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.885' to each side of the equation. 1.885 + -1.885 + x = 0.115 + -1.885 Combine like terms: 1.885 + -1.885 = 0.000 0.000 + x = 0.115 + -1.885 x = 0.115 + -1.885 Combine like terms: 0.115 + -1.885 = -1.77 x = -1.77 Simplifying x = -1.77Subproblem 2
x + 1.885 = -0.115 Simplifying x + 1.885 = -0.115 Reorder the terms: 1.885 + x = -0.115 Solving 1.885 + x = -0.115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.885' to each side of the equation. 1.885 + -1.885 + x = -0.115 + -1.885 Combine like terms: 1.885 + -1.885 = 0.000 0.000 + x = -0.115 + -1.885 x = -0.115 + -1.885 Combine like terms: -0.115 + -1.885 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.77, -2}
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