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Simplifying 2(x2 + 4x + 2.76) = 0 Reorder the terms: 2(2.76 + 4x + x2) = 0 (2.76 * 2 + 4x * 2 + x2 * 2) = 0 (5.52 + 8x + 2x2) = 0 Solving 5.52 + 8x + 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'. 2.76 + 4x + x2 = 0 Move the constant term to the right: Add '-2.76' to each side of the equation. 2.76 + 4x + -2.76 + x2 = 0 + -2.76 Reorder the terms: 2.76 + -2.76 + 4x + x2 = 0 + -2.76 Combine like terms: 2.76 + -2.76 = 0.00 0.00 + 4x + x2 = 0 + -2.76 4x + x2 = 0 + -2.76 Combine like terms: 0 + -2.76 = -2.76 4x + x2 = -2.76 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -2.76 + 4 Reorder the terms: 4 + 4x + x2 = -2.76 + 4 Combine like terms: -2.76 + 4 = 1.24 4 + 4x + x2 = 1.24 Factor a perfect square on the left side: (x + 2)(x + 2) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (x + 2) equal to 1.113552873 and -1.113552873.Subproblem 1
x + 2 = 1.113552873 Simplifying x + 2 = 1.113552873 Reorder the terms: 2 + x = 1.113552873 Solving 2 + x = 1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.113552873 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.113552873 + -2 x = 1.113552873 + -2 Combine like terms: 1.113552873 + -2 = -0.886447127 x = -0.886447127 Simplifying x = -0.886447127Subproblem 2
x + 2 = -1.113552873 Simplifying x + 2 = -1.113552873 Reorder the terms: 2 + x = -1.113552873 Solving 2 + x = -1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.113552873 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.113552873 + -2 x = -1.113552873 + -2 Combine like terms: -1.113552873 + -2 = -3.113552873 x = -3.113552873 Simplifying x = -3.113552873Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.886447127, -3.113552873}
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