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Simplifying x2 + 0.14x + -0.048 = 0 Reorder the terms: -0.048 + 0.14x + x2 = 0 Solving -0.048 + 0.14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.048' to each side of the equation. -0.048 + 0.14x + 0.048 + x2 = 0 + 0.048 Reorder the terms: -0.048 + 0.048 + 0.14x + x2 = 0 + 0.048 Combine like terms: -0.048 + 0.048 = 0.000 0.000 + 0.14x + x2 = 0 + 0.048 0.14x + x2 = 0 + 0.048 Combine like terms: 0 + 0.048 = 0.048 0.14x + x2 = 0.048 The x term is 0.14x. Take half its coefficient (0.07). Square it (0.0049) and add it to both sides. Add '0.0049' to each side of the equation. 0.14x + 0.0049 + x2 = 0.048 + 0.0049 Reorder the terms: 0.0049 + 0.14x + x2 = 0.048 + 0.0049 Combine like terms: 0.048 + 0.0049 = 0.0529 0.0049 + 0.14x + x2 = 0.0529 Factor a perfect square on the left side: (x + 0.07)(x + 0.07) = 0.0529 Calculate the square root of the right side: 0.23 Break this problem into two subproblems by setting (x + 0.07) equal to 0.23 and -0.23.Subproblem 1
x + 0.07 = 0.23 Simplifying x + 0.07 = 0.23 Reorder the terms: 0.07 + x = 0.23 Solving 0.07 + x = 0.23 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07' to each side of the equation. 0.07 + -0.07 + x = 0.23 + -0.07 Combine like terms: 0.07 + -0.07 = 0.00 0.00 + x = 0.23 + -0.07 x = 0.23 + -0.07 Combine like terms: 0.23 + -0.07 = 0.16 x = 0.16 Simplifying x = 0.16Subproblem 2
x + 0.07 = -0.23 Simplifying x + 0.07 = -0.23 Reorder the terms: 0.07 + x = -0.23 Solving 0.07 + x = -0.23 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07' to each side of the equation. 0.07 + -0.07 + x = -0.23 + -0.07 Combine like terms: 0.07 + -0.07 = 0.00 0.00 + x = -0.23 + -0.07 x = -0.23 + -0.07 Combine like terms: -0.23 + -0.07 = -0.3 x = -0.3 Simplifying x = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.16, -0.3}
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