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Simplifying x(x + -5) = 42 Reorder the terms: x(-5 + x) = 42 (-5 * x + x * x) = 42 (-5x + x2) = 42 Solving -5x + x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + -5x + x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + -5x + x2 = 0 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 = 9.446221995 x = 9.446221995 Simplifying x = 9.446221995Subproblem 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 = -4.446221995 x = -4.446221995 Simplifying x = -4.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.446221995, -4.446221995}
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