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Simplifying 2x2 + 8x = 0.2x2 + -4 Reorder the terms: 8x + 2x2 = 0.2x2 + -4 Reorder the terms: 8x + 2x2 = -4 + 0.2x2 Solving 8x + 2x2 = -4 + 0.2x2 Solving for variable 'x'. Reorder the terms: 4 + 8x + 2x2 + -0.2x2 = -4 + 0.2x2 + 4 + -0.2x2 Combine like terms: 2x2 + -0.2x2 = 1.8x2 4 + 8x + 1.8x2 = -4 + 0.2x2 + 4 + -0.2x2 Reorder the terms: 4 + 8x + 1.8x2 = -4 + 4 + 0.2x2 + -0.2x2 Combine like terms: -4 + 4 = 0 4 + 8x + 1.8x2 = 0 + 0.2x2 + -0.2x2 4 + 8x + 1.8x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 4 + 8x + 1.8x2 = 0.0 Begin completing the square. Divide all terms by 1.8 the coefficient of the squared term: Divide each side by '1.8'. 2.222222222 + 4.444444444x + x2 = 0 Move the constant term to the right: Add '-2.222222222' to each side of the equation. 2.222222222 + 4.444444444x + -2.222222222 + x2 = 0 + -2.222222222 Reorder the terms: 2.222222222 + -2.222222222 + 4.444444444x + x2 = 0 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + 4.444444444x + x2 = 0 + -2.222222222 4.444444444x + x2 = 0 + -2.222222222 Combine like terms: 0 + -2.222222222 = -2.222222222 4.444444444x + x2 = -2.222222222 The x term is 4.444444444x. Take half its coefficient (2.222222222). Square it (4.938271604) and add it to both sides. Add '4.938271604' to each side of the equation. 4.444444444x + 4.938271604 + x2 = -2.222222222 + 4.938271604 Reorder the terms: 4.938271604 + 4.444444444x + x2 = -2.222222222 + 4.938271604 Combine like terms: -2.222222222 + 4.938271604 = 2.716049382 4.938271604 + 4.444444444x + x2 = 2.716049382 Factor a perfect square on the left side: (x + 2.222222222)(x + 2.222222222) = 2.716049382 Calculate the square root of the right side: 1.648044108 Break this problem into two subproblems by setting (x + 2.222222222) equal to 1.648044108 and -1.648044108.Subproblem 1
x + 2.222222222 = 1.648044108 Simplifying x + 2.222222222 = 1.648044108 Reorder the terms: 2.222222222 + x = 1.648044108 Solving 2.222222222 + x = 1.648044108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.222222222' to each side of the equation. 2.222222222 + -2.222222222 + x = 1.648044108 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + x = 1.648044108 + -2.222222222 x = 1.648044108 + -2.222222222 Combine like terms: 1.648044108 + -2.222222222 = -0.574178114 x = -0.574178114 Simplifying x = -0.574178114Subproblem 2
x + 2.222222222 = -1.648044108 Simplifying x + 2.222222222 = -1.648044108 Reorder the terms: 2.222222222 + x = -1.648044108 Solving 2.222222222 + x = -1.648044108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.222222222' to each side of the equation. 2.222222222 + -2.222222222 + x = -1.648044108 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + x = -1.648044108 + -2.222222222 x = -1.648044108 + -2.222222222 Combine like terms: -1.648044108 + -2.222222222 = -3.87026633 x = -3.87026633 Simplifying x = -3.87026633Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.574178114, -3.87026633}
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