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Simplifying 49x2 + -28x = 3 Reorder the terms: -28x + 49x2 = 3 Solving -28x + 49x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -28x + 49x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -28x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.0612244898 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.0612244898' to each side of the equation. -0.0612244898 + -0.5714285714x + 0.0612244898 + x2 = 0 + 0.0612244898 Reorder the terms: -0.0612244898 + 0.0612244898 + -0.5714285714x + x2 = 0 + 0.0612244898 Combine like terms: -0.0612244898 + 0.0612244898 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + 0.0612244898 -0.5714285714x + x2 = 0 + 0.0612244898 Combine like terms: 0 + 0.0612244898 = 0.0612244898 -0.5714285714x + x2 = 0.0612244898 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 = 0.0612244898 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 0.0612244898 + 0.08163265305 Combine like terms: 0.0612244898 + 0.08163265305 = 0.14285714285 0.08163265305 + -0.5714285714x + x2 = 0.14285714285 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.14285714285 Calculate the square root of the right side: 0.377964473 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.377964473 and -0.377964473.Subproblem 1
x + -0.2857142857 = 0.377964473 Simplifying x + -0.2857142857 = 0.377964473 Reorder the terms: -0.2857142857 + x = 0.377964473 Solving -0.2857142857 + x = 0.377964473 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 = 0.377964473 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.377964473 + 0.2857142857 x = 0.377964473 + 0.2857142857 Combine like terms: 0.377964473 + 0.2857142857 = 0.6636787587 x = 0.6636787587 Simplifying x = 0.6636787587Subproblem 2
x + -0.2857142857 = -0.377964473 Simplifying x + -0.2857142857 = -0.377964473 Reorder the terms: -0.2857142857 + x = -0.377964473 Solving -0.2857142857 + x = -0.377964473 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 = -0.377964473 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.377964473 + 0.2857142857 x = -0.377964473 + 0.2857142857 Combine like terms: -0.377964473 + 0.2857142857 = -0.0922501873 x = -0.0922501873 Simplifying x = -0.0922501873Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6636787587, -0.0922501873}
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