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Simplifying x2 + 2x + 0.36 = 0 Reorder the terms: 0.36 + 2x + x2 = 0 Solving 0.36 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.36' to each side of the equation. 0.36 + 2x + -0.36 + x2 = 0 + -0.36 Reorder the terms: 0.36 + -0.36 + 2x + x2 = 0 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.00 + 2x + x2 = 0 + -0.36 2x + x2 = 0 + -0.36 Combine like terms: 0 + -0.36 = -0.36 2x + x2 = -0.36 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 = -0.36 + 1 Reorder the terms: 1 + 2x + x2 = -0.36 + 1 Combine like terms: -0.36 + 1 = 0.64 1 + 2x + x2 = 0.64 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.64 Calculate the square root of the right side: 0.8 Break this problem into two subproblems by setting (x + 1) equal to 0.8 and -0.8.Subproblem 1
x + 1 = 0.8 Simplifying x + 1 = 0.8 Reorder the terms: 1 + x = 0.8 Solving 1 + x = 0.8 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 = 0.8 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.8 + -1 x = 0.8 + -1 Combine like terms: 0.8 + -1 = -0.2 x = -0.2 Simplifying x = -0.2Subproblem 2
x + 1 = -0.8 Simplifying x + 1 = -0.8 Reorder the terms: 1 + x = -0.8 Solving 1 + x = -0.8 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 = -0.8 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.8 + -1 x = -0.8 + -1 Combine like terms: -0.8 + -1 = -1.8 x = -1.8 Simplifying x = -1.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2, -1.8}
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