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Simplifying x2 + 3.8x + -32.8 = 0 Reorder the terms: -32.8 + 3.8x + x2 = 0 Solving -32.8 + 3.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32.8' to each side of the equation. -32.8 + 3.8x + 32.8 + x2 = 0 + 32.8 Reorder the terms: -32.8 + 32.8 + 3.8x + x2 = 0 + 32.8 Combine like terms: -32.8 + 32.8 = 0.0 0.0 + 3.8x + x2 = 0 + 32.8 3.8x + x2 = 0 + 32.8 Combine like terms: 0 + 32.8 = 32.8 3.8x + x2 = 32.8 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 = 32.8 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 32.8 + 3.61 Combine like terms: 32.8 + 3.61 = 36.41 3.61 + 3.8x + x2 = 36.41 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 36.41 Calculate the square root of the right side: 6.034069937 Break this problem into two subproblems by setting (x + 1.9) equal to 6.034069937 and -6.034069937.Subproblem 1
x + 1.9 = 6.034069937 Simplifying x + 1.9 = 6.034069937 Reorder the terms: 1.9 + x = 6.034069937 Solving 1.9 + x = 6.034069937 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 = 6.034069937 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 6.034069937 + -1.9 x = 6.034069937 + -1.9 Combine like terms: 6.034069937 + -1.9 = 4.134069937 x = 4.134069937 Simplifying x = 4.134069937Subproblem 2
x + 1.9 = -6.034069937 Simplifying x + 1.9 = -6.034069937 Reorder the terms: 1.9 + x = -6.034069937 Solving 1.9 + x = -6.034069937 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 = -6.034069937 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -6.034069937 + -1.9 x = -6.034069937 + -1.9 Combine like terms: -6.034069937 + -1.9 = -7.934069937 x = -7.934069937 Simplifying x = -7.934069937Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.134069937, -7.934069937}
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