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Simplifying 5x2 + 19x + 2 = 0 Reorder the terms: 2 + 19x + 5x2 = 0 Solving 2 + 19x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 3.8x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 3.8x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 3.8x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 3.8x + x2 = 0 + -0.4 3.8x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 3.8x + x2 = -0.4 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = -0.4 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = -0.4 + 3.61 Combine like terms: -0.4 + 3.61 = 3.21 3.61 + 3.8x + x2 = 3.21 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 3.21 Calculate the square root of the right side: 1.791647287 Break this problem into two subproblems by setting (x + 1.9) equal to 1.791647287 and -1.791647287.Subproblem 1
x + 1.9 = 1.791647287 Simplifying x + 1.9 = 1.791647287 Reorder the terms: 1.9 + x = 1.791647287 Solving 1.9 + x = 1.791647287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 1.791647287 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 1.791647287 + -1.9 x = 1.791647287 + -1.9 Combine like terms: 1.791647287 + -1.9 = -0.108352713 x = -0.108352713 Simplifying x = -0.108352713Subproblem 2
x + 1.9 = -1.791647287 Simplifying x + 1.9 = -1.791647287 Reorder the terms: 1.9 + x = -1.791647287 Solving 1.9 + x = -1.791647287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -1.791647287 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -1.791647287 + -1.9 x = -1.791647287 + -1.9 Combine like terms: -1.791647287 + -1.9 = -3.691647287 x = -3.691647287 Simplifying x = -3.691647287Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.108352713, -3.691647287}
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