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Simplifying 4x2 + 284x + 57 = 0 Reorder the terms: 57 + 284x + 4x2 = 0 Solving 57 + 284x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 14.25 + 71x + x2 = 0 Move the constant term to the right: Add '-14.25' to each side of the equation. 14.25 + 71x + -14.25 + x2 = 0 + -14.25 Reorder the terms: 14.25 + -14.25 + 71x + x2 = 0 + -14.25 Combine like terms: 14.25 + -14.25 = 0.00 0.00 + 71x + x2 = 0 + -14.25 71x + x2 = 0 + -14.25 Combine like terms: 0 + -14.25 = -14.25 71x + x2 = -14.25 The x term is 71x. Take half its coefficient (35.5). Square it (1260.25) and add it to both sides. Add '1260.25' to each side of the equation. 71x + 1260.25 + x2 = -14.25 + 1260.25 Reorder the terms: 1260.25 + 71x + x2 = -14.25 + 1260.25 Combine like terms: -14.25 + 1260.25 = 1246 1260.25 + 71x + x2 = 1246 Factor a perfect square on the left side: (x + 35.5)(x + 35.5) = 1246 Calculate the square root of the right side: 35.298725189 Break this problem into two subproblems by setting (x + 35.5) equal to 35.298725189 and -35.298725189.Subproblem 1
x + 35.5 = 35.298725189 Simplifying x + 35.5 = 35.298725189 Reorder the terms: 35.5 + x = 35.298725189 Solving 35.5 + x = 35.298725189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.5' to each side of the equation. 35.5 + -35.5 + x = 35.298725189 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + x = 35.298725189 + -35.5 x = 35.298725189 + -35.5 Combine like terms: 35.298725189 + -35.5 = -0.201274811 x = -0.201274811 Simplifying x = -0.201274811Subproblem 2
x + 35.5 = -35.298725189 Simplifying x + 35.5 = -35.298725189 Reorder the terms: 35.5 + x = -35.298725189 Solving 35.5 + x = -35.298725189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.5' to each side of the equation. 35.5 + -35.5 + x = -35.298725189 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + x = -35.298725189 + -35.5 x = -35.298725189 + -35.5 Combine like terms: -35.298725189 + -35.5 = -70.798725189 x = -70.798725189 Simplifying x = -70.798725189Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.201274811, -70.798725189}
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