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Simplifying x2 + 6x + -38.5 = 0 Reorder the terms: -38.5 + 6x + x2 = 0 Solving -38.5 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '38.5' to each side of the equation. -38.5 + 6x + 38.5 + x2 = 0 + 38.5 Reorder the terms: -38.5 + 38.5 + 6x + x2 = 0 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + 6x + x2 = 0 + 38.5 6x + x2 = 0 + 38.5 Combine like terms: 0 + 38.5 = 38.5 6x + x2 = 38.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 38.5 + 9 Reorder the terms: 9 + 6x + x2 = 38.5 + 9 Combine like terms: 38.5 + 9 = 47.5 9 + 6x + x2 = 47.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 47.5 Calculate the square root of the right side: 6.892024376 Break this problem into two subproblems by setting (x + 3) equal to 6.892024376 and -6.892024376.Subproblem 1
x + 3 = 6.892024376 Simplifying x + 3 = 6.892024376 Reorder the terms: 3 + x = 6.892024376 Solving 3 + x = 6.892024376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.892024376 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.892024376 + -3 x = 6.892024376 + -3 Combine like terms: 6.892024376 + -3 = 3.892024376 x = 3.892024376 Simplifying x = 3.892024376Subproblem 2
x + 3 = -6.892024376 Simplifying x + 3 = -6.892024376 Reorder the terms: 3 + x = -6.892024376 Solving 3 + x = -6.892024376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.892024376 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.892024376 + -3 x = -6.892024376 + -3 Combine like terms: -6.892024376 + -3 = -9.892024376 x = -9.892024376 Simplifying x = -9.892024376Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.892024376, -9.892024376}
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