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Simplifying 19x2 + 7x + -18 = 0 Reorder the terms: -18 + 7x + 19x2 = 0 Solving -18 + 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'. -0.9473684211 + 0.3684210526x + x2 = 0 Move the constant term to the right: Add '0.9473684211' to each side of the equation. -0.9473684211 + 0.3684210526x + 0.9473684211 + x2 = 0 + 0.9473684211 Reorder the terms: -0.9473684211 + 0.9473684211 + 0.3684210526x + x2 = 0 + 0.9473684211 Combine like terms: -0.9473684211 + 0.9473684211 = 0.0000000000 0.0000000000 + 0.3684210526x + x2 = 0 + 0.9473684211 0.3684210526x + x2 = 0 + 0.9473684211 Combine like terms: 0 + 0.9473684211 = 0.9473684211 0.3684210526x + x2 = 0.9473684211 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 = 0.9473684211 + 0.03393351800 Reorder the terms: 0.03393351800 + 0.3684210526x + x2 = 0.9473684211 + 0.03393351800 Combine like terms: 0.9473684211 + 0.03393351800 = 0.9813019391 0.03393351800 + 0.3684210526x + x2 = 0.9813019391 Factor a perfect square on the left side: (x + 0.1842105263)(x + 0.1842105263) = 0.9813019391 Calculate the square root of the right side: 0.990606854 Break this problem into two subproblems by setting (x + 0.1842105263) equal to 0.990606854 and -0.990606854.Subproblem 1
x + 0.1842105263 = 0.990606854 Simplifying x + 0.1842105263 = 0.990606854 Reorder the terms: 0.1842105263 + x = 0.990606854 Solving 0.1842105263 + x = 0.990606854 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 = 0.990606854 + -0.1842105263 Combine like terms: 0.1842105263 + -0.1842105263 = 0.0000000000 0.0000000000 + x = 0.990606854 + -0.1842105263 x = 0.990606854 + -0.1842105263 Combine like terms: 0.990606854 + -0.1842105263 = 0.8063963277 x = 0.8063963277 Simplifying x = 0.8063963277Subproblem 2
x + 0.1842105263 = -0.990606854 Simplifying x + 0.1842105263 = -0.990606854 Reorder the terms: 0.1842105263 + x = -0.990606854 Solving 0.1842105263 + x = -0.990606854 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 = -0.990606854 + -0.1842105263 Combine like terms: 0.1842105263 + -0.1842105263 = 0.0000000000 0.0000000000 + x = -0.990606854 + -0.1842105263 x = -0.990606854 + -0.1842105263 Combine like terms: -0.990606854 + -0.1842105263 = -1.1748173803 x = -1.1748173803 Simplifying x = -1.1748173803Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8063963277, -1.1748173803}
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