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Simplifying x2 + -0.84x + 0.042 = 0 Reorder the terms: 0.042 + -0.84x + x2 = 0 Solving 0.042 + -0.84x + 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 + -0.84x + -0.042 + x2 = 0 + -0.042 Reorder the terms: 0.042 + -0.042 + -0.84x + x2 = 0 + -0.042 Combine like terms: 0.042 + -0.042 = 0.000 0.000 + -0.84x + x2 = 0 + -0.042 -0.84x + x2 = 0 + -0.042 Combine like terms: 0 + -0.042 = -0.042 -0.84x + x2 = -0.042 The x term is -0.84x. 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. -0.84x + 0.1764 + x2 = -0.042 + 0.1764 Reorder the terms: 0.1764 + -0.84x + x2 = -0.042 + 0.1764 Combine like terms: -0.042 + 0.1764 = 0.1344 0.1764 + -0.84x + x2 = 0.1344 Factor a perfect square on the left side: (x + -0.42)(x + -0.42) = 0.1344 Calculate the square root of the right side: 0.366606056 Break this problem into two subproblems by setting (x + -0.42) equal to 0.366606056 and -0.366606056.Subproblem 1
x + -0.42 = 0.366606056 Simplifying x + -0.42 = 0.366606056 Reorder the terms: -0.42 + x = 0.366606056 Solving -0.42 + x = 0.366606056 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 = 0.366606056 + 0.42 Combine like terms: -0.42 + 0.42 = 0.00 0.00 + x = 0.366606056 + 0.42 x = 0.366606056 + 0.42 Combine like terms: 0.366606056 + 0.42 = 0.786606056 x = 0.786606056 Simplifying x = 0.786606056Subproblem 2
x + -0.42 = -0.366606056 Simplifying x + -0.42 = -0.366606056 Reorder the terms: -0.42 + x = -0.366606056 Solving -0.42 + x = -0.366606056 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 = -0.366606056 + 0.42 Combine like terms: -0.42 + 0.42 = 0.00 0.00 + x = -0.366606056 + 0.42 x = -0.366606056 + 0.42 Combine like terms: -0.366606056 + 0.42 = 0.053393944 x = 0.053393944 Simplifying x = 0.053393944Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.786606056, 0.053393944}
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