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Simplifying 0 = x2 + 2x + 0.4 Reorder the terms: 0 = 0.4 + 2x + x2 Solving 0 = 0.4 + 2x + x2 Solving for variable 'x'. Combine like terms: 0 + -0.4 = -0.4 -0.4 + -2x + -1x2 = 0.4 + 2x + x2 + -0.4 + -2x + -1x2 Reorder the terms: -0.4 + -2x + -1x2 = 0.4 + -0.4 + 2x + -2x + x2 + -1x2 Combine like terms: 0.4 + -0.4 = 0.0 -0.4 + -2x + -1x2 = 0.0 + 2x + -2x + x2 + -1x2 -0.4 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 -0.4 + -2x + -1x2 = 0 + x2 + -1x2 -0.4 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -0.4 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.4 + 2x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 2x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 2x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 2x + x2 = 0 + -0.4 2x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 2x + x2 = -0.4 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.4 + 1 Reorder the terms: 1 + 2x + x2 = -0.4 + 1 Combine like terms: -0.4 + 1 = 0.6 1 + 2x + x2 = 0.6 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.6 Calculate the square root of the right side: 0.774596669 Break this problem into two subproblems by setting (x + 1) equal to 0.774596669 and -0.774596669.Subproblem 1
x + 1 = 0.774596669 Simplifying x + 1 = 0.774596669 Reorder the terms: 1 + x = 0.774596669 Solving 1 + x = 0.774596669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.774596669 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.774596669 + -1 x = 0.774596669 + -1 Combine like terms: 0.774596669 + -1 = -0.225403331 x = -0.225403331 Simplifying x = -0.225403331Subproblem 2
x + 1 = -0.774596669 Simplifying x + 1 = -0.774596669 Reorder the terms: 1 + x = -0.774596669 Solving 1 + x = -0.774596669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.774596669 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.774596669 + -1 x = -0.774596669 + -1 Combine like terms: -0.774596669 + -1 = -1.774596669 x = -1.774596669 Simplifying x = -1.774596669Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.225403331, -1.774596669}
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