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Simplifying 49x2 + 28x + 2 = 0 Reorder the terms: 2 + 28x + 49x2 = 0 Solving 2 + 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'. 0.04081632653 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '-0.04081632653' to each side of the equation. 0.04081632653 + 0.5714285714x + -0.04081632653 + x2 = 0 + -0.04081632653 Reorder the terms: 0.04081632653 + -0.04081632653 + 0.5714285714x + x2 = 0 + -0.04081632653 Combine like terms: 0.04081632653 + -0.04081632653 = 0.00000000000 0.00000000000 + 0.5714285714x + x2 = 0 + -0.04081632653 0.5714285714x + x2 = 0 + -0.04081632653 Combine like terms: 0 + -0.04081632653 = -0.04081632653 0.5714285714x + x2 = -0.04081632653 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 = -0.04081632653 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = -0.04081632653 + 0.08163265305 Combine like terms: -0.04081632653 + 0.08163265305 = 0.04081632652 0.08163265305 + 0.5714285714x + x2 = 0.04081632652 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.04081632652 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.202030509 and -0.202030509.Subproblem 1
x + 0.2857142857 = 0.202030509 Simplifying x + 0.2857142857 = 0.202030509 Reorder the terms: 0.2857142857 + x = 0.202030509 Solving 0.2857142857 + x = 0.202030509 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 = 0.202030509 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.202030509 + -0.2857142857 x = 0.202030509 + -0.2857142857 Combine like terms: 0.202030509 + -0.2857142857 = -0.0836837767 x = -0.0836837767 Simplifying x = -0.0836837767Subproblem 2
x + 0.2857142857 = -0.202030509 Simplifying x + 0.2857142857 = -0.202030509 Reorder the terms: 0.2857142857 + x = -0.202030509 Solving 0.2857142857 + x = -0.202030509 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 = -0.202030509 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.202030509 + -0.2857142857 x = -0.202030509 + -0.2857142857 Combine like terms: -0.202030509 + -0.2857142857 = -0.4877447947 x = -0.4877447947 Simplifying x = -0.4877447947Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0836837767, -0.4877447947}
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