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Simplifying 5x2 + 19x + 3 = 0 Reorder the terms: 3 + 19x + 5x2 = 0 Solving 3 + 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'. 0.6 + 3.8x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 3.8x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 3.8x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 3.8x + x2 = 0 + -0.6 3.8x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 3.8x + x2 = -0.6 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 = -0.6 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = -0.6 + 3.61 Combine like terms: -0.6 + 3.61 = 3.01 3.61 + 3.8x + x2 = 3.01 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 3.01 Calculate the square root of the right side: 1.734935157 Break this problem into two subproblems by setting (x + 1.9) equal to 1.734935157 and -1.734935157.Subproblem 1
x + 1.9 = 1.734935157 Simplifying x + 1.9 = 1.734935157 Reorder the terms: 1.9 + x = 1.734935157 Solving 1.9 + x = 1.734935157 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 = 1.734935157 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 1.734935157 + -1.9 x = 1.734935157 + -1.9 Combine like terms: 1.734935157 + -1.9 = -0.165064843 x = -0.165064843 Simplifying x = -0.165064843Subproblem 2
x + 1.9 = -1.734935157 Simplifying x + 1.9 = -1.734935157 Reorder the terms: 1.9 + x = -1.734935157 Solving 1.9 + x = -1.734935157 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 = -1.734935157 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -1.734935157 + -1.9 x = -1.734935157 + -1.9 Combine like terms: -1.734935157 + -1.9 = -3.634935157 x = -3.634935157 Simplifying x = -3.634935157Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.165064843, -3.634935157}
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