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Simplifying x2 + 0.4x = 0.96 Reorder the terms: 0.4x + x2 = 0.96 Solving 0.4x + x2 = 0.96 Solving for variable 'x'. Reorder the terms: -0.96 + 0.4x + x2 = 0.96 + -0.96 Combine like terms: 0.96 + -0.96 = 0.00 -0.96 + 0.4x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.96' to each side of the equation. -0.96 + 0.4x + 0.96 + x2 = 0.00 + 0.96 Reorder the terms: -0.96 + 0.96 + 0.4x + x2 = 0.00 + 0.96 Combine like terms: -0.96 + 0.96 = 0.00 0.00 + 0.4x + x2 = 0.00 + 0.96 0.4x + x2 = 0.00 + 0.96 Combine like terms: 0.00 + 0.96 = 0.96 0.4x + x2 = 0.96 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.96 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.96 + 0.04 Combine like terms: 0.96 + 0.04 = 1 0.04 + 0.4x + x2 = 1 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + 0.2) equal to 1 and -1.Subproblem 1
x + 0.2 = 1 Simplifying x + 0.2 = 1 Reorder the terms: 0.2 + x = 1 Solving 0.2 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1 + -0.2 x = 1 + -0.2 Combine like terms: 1 + -0.2 = 0.8 x = 0.8 Simplifying x = 0.8Subproblem 2
x + 0.2 = -1 Simplifying x + 0.2 = -1 Reorder the terms: 0.2 + x = -1 Solving 0.2 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1 + -0.2 x = -1 + -0.2 Combine like terms: -1 + -0.2 = -1.2 x = -1.2 Simplifying x = -1.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8, -1.2}
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