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Simplifying 19x2 + 7x + -34 = 0 Reorder the terms: -34 + 7x + 19x2 = 0 Solving -34 + 7x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -1.789473684 + 0.3684210526x + x2 = 0 Move the constant term to the right: Add '1.789473684' to each side of the equation. -1.789473684 + 0.3684210526x + 1.789473684 + x2 = 0 + 1.789473684 Reorder the terms: -1.789473684 + 1.789473684 + 0.3684210526x + x2 = 0 + 1.789473684 Combine like terms: -1.789473684 + 1.789473684 = 0.000000000 0.000000000 + 0.3684210526x + x2 = 0 + 1.789473684 0.3684210526x + x2 = 0 + 1.789473684 Combine like terms: 0 + 1.789473684 = 1.789473684 0.3684210526x + x2 = 1.789473684 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 = 1.789473684 + 0.03393351800 Reorder the terms: 0.03393351800 + 0.3684210526x + x2 = 1.789473684 + 0.03393351800 Combine like terms: 1.789473684 + 0.03393351800 = 1.823407202 0.03393351800 + 0.3684210526x + x2 = 1.823407202 Factor a perfect square on the left side: (x + 0.1842105263)(x + 0.1842105263) = 1.823407202 Calculate the square root of the right side: 1.350335959 Break this problem into two subproblems by setting (x + 0.1842105263) equal to 1.350335959 and -1.350335959.Subproblem 1
x + 0.1842105263 = 1.350335959 Simplifying x + 0.1842105263 = 1.350335959 Reorder the terms: 0.1842105263 + x = 1.350335959 Solving 0.1842105263 + x = 1.350335959 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 = 1.350335959 + -0.1842105263 Combine like terms: 0.1842105263 + -0.1842105263 = 0.0000000000 0.0000000000 + x = 1.350335959 + -0.1842105263 x = 1.350335959 + -0.1842105263 Combine like terms: 1.350335959 + -0.1842105263 = 1.1661254327 x = 1.1661254327 Simplifying x = 1.1661254327Subproblem 2
x + 0.1842105263 = -1.350335959 Simplifying x + 0.1842105263 = -1.350335959 Reorder the terms: 0.1842105263 + x = -1.350335959 Solving 0.1842105263 + x = -1.350335959 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 = -1.350335959 + -0.1842105263 Combine like terms: 0.1842105263 + -0.1842105263 = 0.0000000000 0.0000000000 + x = -1.350335959 + -0.1842105263 x = -1.350335959 + -0.1842105263 Combine like terms: -1.350335959 + -0.1842105263 = -1.5345464853 x = -1.5345464853 Simplifying x = -1.5345464853Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1661254327, -1.5345464853}
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