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Simplifying 28x2 + 97x + 4 = 0 Reorder the terms: 4 + 97x + 28x2 = 0 Solving 4 + 97x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.1428571429 + 3.464285714x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 3.464285714x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 3.464285714x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 3.464285714x + x2 = 0 + -0.1428571429 3.464285714x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 3.464285714x + x2 = -0.1428571429 The x term is 3.464285714x. Take half its coefficient (1.732142857). Square it (3.000318877) and add it to both sides. Add '3.000318877' to each side of the equation. 3.464285714x + 3.000318877 + x2 = -0.1428571429 + 3.000318877 Reorder the terms: 3.000318877 + 3.464285714x + x2 = -0.1428571429 + 3.000318877 Combine like terms: -0.1428571429 + 3.000318877 = 2.8574617341 3.000318877 + 3.464285714x + x2 = 2.8574617341 Factor a perfect square on the left side: (x + 1.732142857)(x + 1.732142857) = 2.8574617341 Calculate the square root of the right side: 1.690402832 Break this problem into two subproblems by setting (x + 1.732142857) equal to 1.690402832 and -1.690402832.Subproblem 1
x + 1.732142857 = 1.690402832 Simplifying x + 1.732142857 = 1.690402832 Reorder the terms: 1.732142857 + x = 1.690402832 Solving 1.732142857 + x = 1.690402832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.732142857' to each side of the equation. 1.732142857 + -1.732142857 + x = 1.690402832 + -1.732142857 Combine like terms: 1.732142857 + -1.732142857 = 0.000000000 0.000000000 + x = 1.690402832 + -1.732142857 x = 1.690402832 + -1.732142857 Combine like terms: 1.690402832 + -1.732142857 = -0.041740025 x = -0.041740025 Simplifying x = -0.041740025Subproblem 2
x + 1.732142857 = -1.690402832 Simplifying x + 1.732142857 = -1.690402832 Reorder the terms: 1.732142857 + x = -1.690402832 Solving 1.732142857 + x = -1.690402832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.732142857' to each side of the equation. 1.732142857 + -1.732142857 + x = -1.690402832 + -1.732142857 Combine like terms: 1.732142857 + -1.732142857 = 0.000000000 0.000000000 + x = -1.690402832 + -1.732142857 x = -1.690402832 + -1.732142857 Combine like terms: -1.690402832 + -1.732142857 = -3.422545689 x = -3.422545689 Simplifying x = -3.422545689Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.041740025, -3.422545689}
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