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Simplifying 49x2 + 28x + 4 = 24 Reorder the terms: 4 + 28x + 49x2 = 24 Solving 4 + 28x + 49x2 = 24 Solving for variable 'x'. Reorder the terms: 4 + -24 + 28x + 49x2 = 24 + -24 Combine like terms: 4 + -24 = -20 -20 + 28x + 49x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -20 + 28x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.4081632653 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.5714285714x + 0.4081632653 + x2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + 0.5714285714x + x2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + 0.4081632653 0.5714285714x + x2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 0.5714285714x + x2 = 0.4081632653 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 = 0.4081632653 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 0.4081632653 + 0.08163265305 Combine like terms: 0.4081632653 + 0.08163265305 = 0.48979591835 0.08163265305 + 0.5714285714x + x2 = 0.48979591835 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.48979591835 Calculate the square root of the right side: 0.699854212 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.699854212 and -0.699854212.Subproblem 1
x + 0.2857142857 = 0.699854212 Simplifying x + 0.2857142857 = 0.699854212 Reorder the terms: 0.2857142857 + x = 0.699854212 Solving 0.2857142857 + x = 0.699854212 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 = 0.699854212 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.699854212 + -0.2857142857 x = 0.699854212 + -0.2857142857 Combine like terms: 0.699854212 + -0.2857142857 = 0.4141399263 x = 0.4141399263 Simplifying x = 0.4141399263Subproblem 2
x + 0.2857142857 = -0.699854212 Simplifying x + 0.2857142857 = -0.699854212 Reorder the terms: 0.2857142857 + x = -0.699854212 Solving 0.2857142857 + x = -0.699854212 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 = -0.699854212 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.699854212 + -0.2857142857 x = -0.699854212 + -0.2857142857 Combine like terms: -0.699854212 + -0.2857142857 = -0.9855684977 x = -0.9855684977 Simplifying x = -0.9855684977Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4141399263, -0.9855684977}
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