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Simplifying x2 + 5x + -42 = 0 Reorder the terms: -42 + 5x + x2 = 0 Solving -42 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 5x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 5x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 5x + x2 = 0 + 42 5x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 5x + x2 = 42 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 42 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 42 + 6.25 Combine like terms: 42 + 6.25 = 48.25 6.25 + 5x + x2 = 48.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + 2.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + 2.5 = 6.946221995 Simplifying x + 2.5 = 6.946221995 Reorder the terms: 2.5 + x = 6.946221995 Solving 2.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.946221995 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.946221995 + -2.5 x = 6.946221995 + -2.5 Combine like terms: 6.946221995 + -2.5 = 4.446221995 x = 4.446221995 Simplifying x = 4.446221995Subproblem 2
x + 2.5 = -6.946221995 Simplifying x + 2.5 = -6.946221995 Reorder the terms: 2.5 + x = -6.946221995 Solving 2.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.946221995 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.946221995 + -2.5 x = -6.946221995 + -2.5 Combine like terms: -6.946221995 + -2.5 = -9.446221995 x = -9.446221995 Simplifying x = -9.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.446221995, -9.446221995}
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