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Simplifying x2 + -40x + -48 = 0 Reorder the terms: -48 + -40x + x2 = 0 Solving -48 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -40x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -40x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -40x + x2 = 0 + 48 -40x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -40x + x2 = 48 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 48 + 400 Reorder the terms: 400 + -40x + x2 = 48 + 400 Combine like terms: 48 + 400 = 448 400 + -40x + x2 = 448 Factor a perfect square on the left side: (x + -20)(x + -20) = 448 Calculate the square root of the right side: 21.166010489 Break this problem into two subproblems by setting (x + -20) equal to 21.166010489 and -21.166010489.Subproblem 1
x + -20 = 21.166010489 Simplifying x + -20 = 21.166010489 Reorder the terms: -20 + x = 21.166010489 Solving -20 + x = 21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 21.166010489 + 20 Combine like terms: -20 + 20 = 0 0 + x = 21.166010489 + 20 x = 21.166010489 + 20 Combine like terms: 21.166010489 + 20 = 41.166010489 x = 41.166010489 Simplifying x = 41.166010489Subproblem 2
x + -20 = -21.166010489 Simplifying x + -20 = -21.166010489 Reorder the terms: -20 + x = -21.166010489 Solving -20 + x = -21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -21.166010489 + 20 Combine like terms: -20 + 20 = 0 0 + x = -21.166010489 + 20 x = -21.166010489 + 20 Combine like terms: -21.166010489 + 20 = -1.166010489 x = -1.166010489 Simplifying x = -1.166010489Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.166010489, -1.166010489}
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