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Simplifying x2 + 0.16x + -0.042 = 0 Reorder the terms: -0.042 + 0.16x + x2 = 0 Solving -0.042 + 0.16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.042' to each side of the equation. -0.042 + 0.16x + 0.042 + x2 = 0 + 0.042 Reorder the terms: -0.042 + 0.042 + 0.16x + x2 = 0 + 0.042 Combine like terms: -0.042 + 0.042 = 0.000 0.000 + 0.16x + x2 = 0 + 0.042 0.16x + x2 = 0 + 0.042 Combine like terms: 0 + 0.042 = 0.042 0.16x + x2 = 0.042 The x term is 0.16x. Take half its coefficient (0.08). Square it (0.0064) and add it to both sides. Add '0.0064' to each side of the equation. 0.16x + 0.0064 + x2 = 0.042 + 0.0064 Reorder the terms: 0.0064 + 0.16x + x2 = 0.042 + 0.0064 Combine like terms: 0.042 + 0.0064 = 0.0484 0.0064 + 0.16x + x2 = 0.0484 Factor a perfect square on the left side: (x + 0.08)(x + 0.08) = 0.0484 Calculate the square root of the right side: 0.22 Break this problem into two subproblems by setting (x + 0.08) equal to 0.22 and -0.22.Subproblem 1
x + 0.08 = 0.22 Simplifying x + 0.08 = 0.22 Reorder the terms: 0.08 + x = 0.22 Solving 0.08 + x = 0.22 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + x = 0.22 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + x = 0.22 + -0.08 x = 0.22 + -0.08 Combine like terms: 0.22 + -0.08 = 0.14 x = 0.14 Simplifying x = 0.14Subproblem 2
x + 0.08 = -0.22 Simplifying x + 0.08 = -0.22 Reorder the terms: 0.08 + x = -0.22 Solving 0.08 + x = -0.22 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08' to each side of the equation. 0.08 + -0.08 + x = -0.22 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + x = -0.22 + -0.08 x = -0.22 + -0.08 Combine like terms: -0.22 + -0.08 = -0.3 x = -0.3 Simplifying x = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.14, -0.3}
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