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Simplifying x2 + 0.7x + 0.1 = 0 Reorder the terms: 0.1 + 0.7x + x2 = 0 Solving 0.1 + 0.7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 0.7x + -0.1 + x2 = 0 + -0.1 Reorder the terms: 0.1 + -0.1 + 0.7x + x2 = 0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 0.7x + x2 = 0 + -0.1 0.7x + x2 = 0 + -0.1 Combine like terms: 0 + -0.1 = -0.1 0.7x + x2 = -0.1 The x term is 0.7x. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7x + 0.1225 + x2 = -0.1 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = -0.1 + 0.1225 Combine like terms: -0.1 + 0.1225 = 0.0225 0.1225 + 0.7x + x2 = 0.0225 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 0.0225 Calculate the square root of the right side: 0.15 Break this problem into two subproblems by setting (x + 0.35) equal to 0.15 and -0.15.Subproblem 1
x + 0.35 = 0.15 Simplifying x + 0.35 = 0.15 Reorder the terms: 0.35 + x = 0.15 Solving 0.35 + x = 0.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 0.15 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 0.15 + -0.35 x = 0.15 + -0.35 Combine like terms: 0.15 + -0.35 = -0.2 x = -0.2 Simplifying x = -0.2Subproblem 2
x + 0.35 = -0.15 Simplifying x + 0.35 = -0.15 Reorder the terms: 0.35 + x = -0.15 Solving 0.35 + x = -0.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -0.15 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -0.15 + -0.35 x = -0.15 + -0.35 Combine like terms: -0.15 + -0.35 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2, -0.5}
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