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Simplifying 7 = 19(x * x) + 7x + 2 Multiply x * x 7 = 19(x2) + 7x + 2 Reorder the terms: 7 = 2 + 7x + 19x2 Solving 7 = 2 + 7x + 19x2 Solving for variable 'x'. Combine like terms: 7 + -2 = 5 5 + -7x + -19x2 = 2 + 7x + 19x2 + -2 + -7x + -19x2 Reorder the terms: 5 + -7x + -19x2 = 2 + -2 + 7x + -7x + 19x2 + -19x2 Combine like terms: 2 + -2 = 0 5 + -7x + -19x2 = 0 + 7x + -7x + 19x2 + -19x2 5 + -7x + -19x2 = 7x + -7x + 19x2 + -19x2 Combine like terms: 7x + -7x = 0 5 + -7x + -19x2 = 0 + 19x2 + -19x2 5 + -7x + -19x2 = 19x2 + -19x2 Combine like terms: 19x2 + -19x2 = 0 5 + -7x + -19x2 = 0 Begin completing the square. Divide all terms by -19 the coefficient of the squared term: Divide each side by '-19'. -0.2631578947 + 0.3684210526x + x2 = 0 Move the constant term to the right: Add '0.2631578947' to each side of the equation. -0.2631578947 + 0.3684210526x + 0.2631578947 + x2 = 0 + 0.2631578947 Reorder the terms: -0.2631578947 + 0.2631578947 + 0.3684210526x + x2 = 0 + 0.2631578947 Combine like terms: -0.2631578947 + 0.2631578947 = 0.0000000000 0.0000000000 + 0.3684210526x + x2 = 0 + 0.2631578947 0.3684210526x + x2 = 0 + 0.2631578947 Combine like terms: 0 + 0.2631578947 = 0.2631578947 0.3684210526x + x2 = 0.2631578947 The x term is 0.3684210526x. Take half its coefficient (0.1842105263). Square it (0.03393351800) and add it to both sides. Add '0.03393351800' to each side of the equation. 0.3684210526x + 0.03393351800 + x2 = 0.2631578947 + 0.03393351800 Reorder the terms: 0.03393351800 + 0.3684210526x + x2 = 0.2631578947 + 0.03393351800 Combine like terms: 0.2631578947 + 0.03393351800 = 0.2970914127 0.03393351800 + 0.3684210526x + x2 = 0.2970914127 Factor a perfect square on the left side: (x + 0.1842105263)(x + 0.1842105263) = 0.2970914127 Calculate the square root of the right side: 0.545060926 Break this problem into two subproblems by setting (x + 0.1842105263) equal to 0.545060926 and -0.545060926.Subproblem 1
x + 0.1842105263 = 0.545060926 Simplifying x + 0.1842105263 = 0.545060926 Reorder the terms: 0.1842105263 + x = 0.545060926 Solving 0.1842105263 + x = 0.545060926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1842105263' to each side of the equation. 0.1842105263 + -0.1842105263 + x = 0.545060926 + -0.1842105263 Combine like terms: 0.1842105263 + -0.1842105263 = 0.0000000000 0.0000000000 + x = 0.545060926 + -0.1842105263 x = 0.545060926 + -0.1842105263 Combine like terms: 0.545060926 + -0.1842105263 = 0.3608503997 x = 0.3608503997 Simplifying x = 0.3608503997Subproblem 2
x + 0.1842105263 = -0.545060926 Simplifying x + 0.1842105263 = -0.545060926 Reorder the terms: 0.1842105263 + x = -0.545060926 Solving 0.1842105263 + x = -0.545060926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1842105263' to each side of the equation. 0.1842105263 + -0.1842105263 + x = -0.545060926 + -0.1842105263 Combine like terms: 0.1842105263 + -0.1842105263 = 0.0000000000 0.0000000000 + x = -0.545060926 + -0.1842105263 x = -0.545060926 + -0.1842105263 Combine like terms: -0.545060926 + -0.1842105263 = -0.7292714523 x = -0.7292714523 Simplifying x = -0.7292714523Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3608503997, -0.7292714523}
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