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Simplifying 7x2 + 4x = 1 Reorder the terms: 4x + 7x2 = 1 Solving 4x + 7x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 4x + 7x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.5714285714x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 0.5714285714x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + 0.1428571429 0.5714285714x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 0.5714285714x + x2 = 0.1428571429 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 = 0.1428571429 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 0.1428571429 + 0.08163265305 Combine like terms: 0.1428571429 + 0.08163265305 = 0.22448979595 0.08163265305 + 0.5714285714x + x2 = 0.22448979595 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.22448979595 Calculate the square root of the right side: 0.473803542 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.473803542 and -0.473803542.Subproblem 1
x + 0.2857142857 = 0.473803542 Simplifying x + 0.2857142857 = 0.473803542 Reorder the terms: 0.2857142857 + x = 0.473803542 Solving 0.2857142857 + x = 0.473803542 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 = 0.473803542 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.473803542 + -0.2857142857 x = 0.473803542 + -0.2857142857 Combine like terms: 0.473803542 + -0.2857142857 = 0.1880892563 x = 0.1880892563 Simplifying x = 0.1880892563Subproblem 2
x + 0.2857142857 = -0.473803542 Simplifying x + 0.2857142857 = -0.473803542 Reorder the terms: 0.2857142857 + x = -0.473803542 Solving 0.2857142857 + x = -0.473803542 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 = -0.473803542 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.473803542 + -0.2857142857 x = -0.473803542 + -0.2857142857 Combine like terms: -0.473803542 + -0.2857142857 = -0.7595178277 x = -0.7595178277 Simplifying x = -0.7595178277Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1880892563, -0.7595178277}
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