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Simplifying x2 + 0.840x + -0.1764 = 0 Reorder the terms: -0.1764 + 0.840x + x2 = 0 Solving -0.1764 + 0.840x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.1764' to each side of the equation. -0.1764 + 0.840x + 0.1764 + x2 = 0 + 0.1764 Reorder the terms: -0.1764 + 0.1764 + 0.840x + x2 = 0 + 0.1764 Combine like terms: -0.1764 + 0.1764 = 0.0000 0.0000 + 0.840x + x2 = 0 + 0.1764 0.840x + x2 = 0 + 0.1764 Combine like terms: 0 + 0.1764 = 0.1764 0.840x + x2 = 0.1764 The x term is 0.840x. Take half its coefficient (0.42). Square it (0.1764) and add it to both sides. Add '0.1764' to each side of the equation. 0.840x + 0.1764 + x2 = 0.1764 + 0.1764 Reorder the terms: 0.1764 + 0.840x + x2 = 0.1764 + 0.1764 Combine like terms: 0.1764 + 0.1764 = 0.3528 0.1764 + 0.840x + x2 = 0.3528 Factor a perfect square on the left side: (x + 0.42)(x + 0.42) = 0.3528 Calculate the square root of the right side: 0.593969696 Break this problem into two subproblems by setting (x + 0.42) equal to 0.593969696 and -0.593969696.Subproblem 1
x + 0.42 = 0.593969696 Simplifying x + 0.42 = 0.593969696 Reorder the terms: 0.42 + x = 0.593969696 Solving 0.42 + x = 0.593969696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.42' to each side of the equation. 0.42 + -0.42 + x = 0.593969696 + -0.42 Combine like terms: 0.42 + -0.42 = 0.00 0.00 + x = 0.593969696 + -0.42 x = 0.593969696 + -0.42 Combine like terms: 0.593969696 + -0.42 = 0.173969696 x = 0.173969696 Simplifying x = 0.173969696Subproblem 2
x + 0.42 = -0.593969696 Simplifying x + 0.42 = -0.593969696 Reorder the terms: 0.42 + x = -0.593969696 Solving 0.42 + x = -0.593969696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.42' to each side of the equation. 0.42 + -0.42 + x = -0.593969696 + -0.42 Combine like terms: 0.42 + -0.42 = 0.00 0.00 + x = -0.593969696 + -0.42 x = -0.593969696 + -0.42 Combine like terms: -0.593969696 + -0.42 = -1.013969696 x = -1.013969696 Simplifying x = -1.013969696Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.173969696, -1.013969696}
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