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Simplifying x2 + 3.8x + -47.272 = 0 Reorder the terms: -47.272 + 3.8x + x2 = 0 Solving -47.272 + 3.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '47.272' to each side of the equation. -47.272 + 3.8x + 47.272 + x2 = 0 + 47.272 Reorder the terms: -47.272 + 47.272 + 3.8x + x2 = 0 + 47.272 Combine like terms: -47.272 + 47.272 = 0.000 0.000 + 3.8x + x2 = 0 + 47.272 3.8x + x2 = 0 + 47.272 Combine like terms: 0 + 47.272 = 47.272 3.8x + x2 = 47.272 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 = 47.272 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 47.272 + 3.61 Combine like terms: 47.272 + 3.61 = 50.882 3.61 + 3.8x + x2 = 50.882 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 50.882 Calculate the square root of the right side: 7.133161992 Break this problem into two subproblems by setting (x + 1.9) equal to 7.133161992 and -7.133161992.Subproblem 1
x + 1.9 = 7.133161992 Simplifying x + 1.9 = 7.133161992 Reorder the terms: 1.9 + x = 7.133161992 Solving 1.9 + x = 7.133161992 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 = 7.133161992 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 7.133161992 + -1.9 x = 7.133161992 + -1.9 Combine like terms: 7.133161992 + -1.9 = 5.233161992 x = 5.233161992 Simplifying x = 5.233161992Subproblem 2
x + 1.9 = -7.133161992 Simplifying x + 1.9 = -7.133161992 Reorder the terms: 1.9 + x = -7.133161992 Solving 1.9 + x = -7.133161992 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 = -7.133161992 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -7.133161992 + -1.9 x = -7.133161992 + -1.9 Combine like terms: -7.133161992 + -1.9 = -9.033161992 x = -9.033161992 Simplifying x = -9.033161992Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.233161992, -9.033161992}
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