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Simplifying X(X + -3) = 42 Reorder the terms: X(-3 + X) = 42 (-3 * X + X * X) = 42 (-3X + X2) = 42 Solving -3X + X2 = 42 Solving for variable 'X'. Reorder the terms: -42 + -3X + X2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + -3X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -3X + 42 + X2 = 0 + 42 Reorder the terms: -42 + 42 + -3X + X2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -3X + X2 = 0 + 42 -3X + X2 = 0 + 42 Combine like terms: 0 + 42 = 42 -3X + X2 = 42 The X term is -3X. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3X + 2.25 + X2 = 42 + 2.25 Reorder the terms: 2.25 + -3X + X2 = 42 + 2.25 Combine like terms: 42 + 2.25 = 44.25 2.25 + -3X + X2 = 44.25 Factor a perfect square on the left side: (X + -1.5)(X + -1.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (X + -1.5) equal to 6.652067348 and -6.652067348.Subproblem 1
X + -1.5 = 6.652067348 Simplifying X + -1.5 = 6.652067348 Reorder the terms: -1.5 + X = 6.652067348 Solving -1.5 + X = 6.652067348 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + X = 6.652067348 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = 6.652067348 + 1.5 X = 6.652067348 + 1.5 Combine like terms: 6.652067348 + 1.5 = 8.152067348 X = 8.152067348 Simplifying X = 8.152067348Subproblem 2
X + -1.5 = -6.652067348 Simplifying X + -1.5 = -6.652067348 Reorder the terms: -1.5 + X = -6.652067348 Solving -1.5 + X = -6.652067348 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + X = -6.652067348 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = -6.652067348 + 1.5 X = -6.652067348 + 1.5 Combine like terms: -6.652067348 + 1.5 = -5.152067348 X = -5.152067348 Simplifying X = -5.152067348Solution
The solution to the problem is based on the solutions from the subproblems. X = {8.152067348, -5.152067348}
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