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Simplifying 0.2x + x2 = 0.99 Solving 0.2x + x2 = 0.99 Solving for variable 'x'. Reorder the terms: -0.99 + 0.2x + x2 = 0.99 + -0.99 Combine like terms: 0.99 + -0.99 = 0.00 -0.99 + 0.2x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.99' to each side of the equation. -0.99 + 0.2x + 0.99 + x2 = 0.00 + 0.99 Reorder the terms: -0.99 + 0.99 + 0.2x + x2 = 0.00 + 0.99 Combine like terms: -0.99 + 0.99 = 0.00 0.00 + 0.2x + x2 = 0.00 + 0.99 0.2x + x2 = 0.00 + 0.99 Combine like terms: 0.00 + 0.99 = 0.99 0.2x + x2 = 0.99 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 = 0.99 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.99 + 0.01 Combine like terms: 0.99 + 0.01 = 1 0.01 + 0.2x + x2 = 1 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + 0.1) equal to 1 and -1.Subproblem 1
x + 0.1 = 1 Simplifying x + 0.1 = 1 Reorder the terms: 0.1 + x = 1 Solving 0.1 + x = 1 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 = 1 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1 + -0.1 x = 1 + -0.1 Combine like terms: 1 + -0.1 = 0.9 x = 0.9 Simplifying x = 0.9Subproblem 2
x + 0.1 = -1 Simplifying x + 0.1 = -1 Reorder the terms: 0.1 + x = -1 Solving 0.1 + x = -1 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 = -1 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1 + -0.1 x = -1 + -0.1 Combine like terms: -1 + -0.1 = -1.1 x = -1.1 Simplifying x = -1.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9, -1.1}
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