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Simplifying x2 + 0.2x = 0.35 Reorder the terms: 0.2x + x2 = 0.35 Solving 0.2x + x2 = 0.35 Solving for variable 'x'. Reorder the terms: -0.35 + 0.2x + x2 = 0.35 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 -0.35 + 0.2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + 0.2x + 0.35 + x2 = 0.00 + 0.35 Reorder the terms: -0.35 + 0.35 + 0.2x + x2 = 0.00 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + 0.2x + x2 = 0.00 + 0.35 0.2x + x2 = 0.00 + 0.35 Combine like terms: 0.00 + 0.35 = 0.35 0.2x + x2 = 0.35 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 0.35 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.35 + 0.01 Combine like terms: 0.35 + 0.01 = 0.36 0.01 + 0.2x + x2 = 0.36 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.36 Calculate the square root of the right side: 0.6 Break this problem into two subproblems by setting (x + 0.1) equal to 0.6 and -0.6.Subproblem 1
x + 0.1 = 0.6 Simplifying x + 0.1 = 0.6 Reorder the terms: 0.1 + x = 0.6 Solving 0.1 + x = 0.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.6 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.6 + -0.1 x = 0.6 + -0.1 Combine like terms: 0.6 + -0.1 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 0.1 = -0.6 Simplifying x + 0.1 = -0.6 Reorder the terms: 0.1 + x = -0.6 Solving 0.1 + x = -0.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.6 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.6 + -0.1 x = -0.6 + -0.1 Combine like terms: -0.6 + -0.1 = -0.7 x = -0.7 Simplifying x = -0.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -0.7}
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