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Simplifying 14x2 + 4x + -7 = 4 Reorder the terms: -7 + 4x + 14x2 = 4 Solving -7 + 4x + 14x2 = 4 Solving for variable 'x'. Reorder the terms: -7 + -4 + 4x + 14x2 = 4 + -4 Combine like terms: -7 + -4 = -11 -11 + 4x + 14x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -11 + 4x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.7857142857 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.7857142857' to each side of the equation. -0.7857142857 + 0.2857142857x + 0.7857142857 + x2 = 0 + 0.7857142857 Reorder the terms: -0.7857142857 + 0.7857142857 + 0.2857142857x + x2 = 0 + 0.7857142857 Combine like terms: -0.7857142857 + 0.7857142857 = 0.0000000000 0.0000000000 + 0.2857142857x + x2 = 0 + 0.7857142857 0.2857142857x + x2 = 0 + 0.7857142857 Combine like terms: 0 + 0.7857142857 = 0.7857142857 0.2857142857x + x2 = 0.7857142857 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = 0.7857142857 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 0.7857142857 + 0.02040816328 Combine like terms: 0.7857142857 + 0.02040816328 = 0.80612244898 0.02040816328 + 0.2857142857x + x2 = 0.80612244898 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 0.80612244898 Calculate the square root of the right side: 0.897843221 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 0.897843221 and -0.897843221.Subproblem 1
x + 0.1428571429 = 0.897843221 Simplifying x + 0.1428571429 = 0.897843221 Reorder the terms: 0.1428571429 + x = 0.897843221 Solving 0.1428571429 + x = 0.897843221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = 0.897843221 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 0.897843221 + -0.1428571429 x = 0.897843221 + -0.1428571429 Combine like terms: 0.897843221 + -0.1428571429 = 0.7549860781 x = 0.7549860781 Simplifying x = 0.7549860781Subproblem 2
x + 0.1428571429 = -0.897843221 Simplifying x + 0.1428571429 = -0.897843221 Reorder the terms: 0.1428571429 + x = -0.897843221 Solving 0.1428571429 + x = -0.897843221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = -0.897843221 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -0.897843221 + -0.1428571429 x = -0.897843221 + -0.1428571429 Combine like terms: -0.897843221 + -0.1428571429 = -1.0407003639 x = -1.0407003639 Simplifying x = -1.0407003639Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7549860781, -1.0407003639}
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