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Simplifying x2 + 40x + -480 = 0 Reorder the terms: -480 + 40x + x2 = 0 Solving -480 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '480' to each side of the equation. -480 + 40x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 40x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 40x + x2 = 0 + 480 40x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 40x + x2 = 480 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 = 480 + 400 Reorder the terms: 400 + 40x + x2 = 480 + 400 Combine like terms: 480 + 400 = 880 400 + 40x + x2 = 880 Factor a perfect square on the left side: (x + 20)(x + 20) = 880 Calculate the square root of the right side: 29.664793948 Break this problem into two subproblems by setting (x + 20) equal to 29.664793948 and -29.664793948.Subproblem 1
x + 20 = 29.664793948 Simplifying x + 20 = 29.664793948 Reorder the terms: 20 + x = 29.664793948 Solving 20 + x = 29.664793948 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 = 29.664793948 + -20 Combine like terms: 20 + -20 = 0 0 + x = 29.664793948 + -20 x = 29.664793948 + -20 Combine like terms: 29.664793948 + -20 = 9.664793948 x = 9.664793948 Simplifying x = 9.664793948Subproblem 2
x + 20 = -29.664793948 Simplifying x + 20 = -29.664793948 Reorder the terms: 20 + x = -29.664793948 Solving 20 + x = -29.664793948 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 = -29.664793948 + -20 Combine like terms: 20 + -20 = 0 0 + x = -29.664793948 + -20 x = -29.664793948 + -20 Combine like terms: -29.664793948 + -20 = -49.664793948 x = -49.664793948 Simplifying x = -49.664793948Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.664793948, -49.664793948}
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