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Simplifying 49x2 + -28x + -44 = 0 Reorder the terms: -44 + -28x + 49x2 = 0 Solving -44 + -28x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.8979591837 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.8979591837' to each side of the equation. -0.8979591837 + -0.5714285714x + 0.8979591837 + x2 = 0 + 0.8979591837 Reorder the terms: -0.8979591837 + 0.8979591837 + -0.5714285714x + x2 = 0 + 0.8979591837 Combine like terms: -0.8979591837 + 0.8979591837 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + 0.8979591837 -0.5714285714x + x2 = 0 + 0.8979591837 Combine like terms: 0 + 0.8979591837 = 0.8979591837 -0.5714285714x + x2 = 0.8979591837 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 0.8979591837 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 0.8979591837 + 0.08163265305 Combine like terms: 0.8979591837 + 0.08163265305 = 0.97959183675 0.08163265305 + -0.5714285714x + x2 = 0.97959183675 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.97959183675 Calculate the square root of the right side: 0.989743319 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.989743319 and -0.989743319.Subproblem 1
x + -0.2857142857 = 0.989743319 Simplifying x + -0.2857142857 = 0.989743319 Reorder the terms: -0.2857142857 + x = 0.989743319 Solving -0.2857142857 + x = 0.989743319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 0.989743319 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.989743319 + 0.2857142857 x = 0.989743319 + 0.2857142857 Combine like terms: 0.989743319 + 0.2857142857 = 1.2754576047 x = 1.2754576047 Simplifying x = 1.2754576047Subproblem 2
x + -0.2857142857 = -0.989743319 Simplifying x + -0.2857142857 = -0.989743319 Reorder the terms: -0.2857142857 + x = -0.989743319 Solving -0.2857142857 + x = -0.989743319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -0.989743319 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.989743319 + 0.2857142857 x = -0.989743319 + 0.2857142857 Combine like terms: -0.989743319 + 0.2857142857 = -0.7040290333 x = -0.7040290333 Simplifying x = -0.7040290333Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2754576047, -0.7040290333}
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