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Simplifying 0 = 1x2 + 4x + -405 Reorder the terms: 0 = -405 + 4x + 1x2 Solving 0 = -405 + 4x + 1x2 Solving for variable 'x'. Combine like terms: 0 + 405 = 405 405 + -4x + -1x2 = -405 + 4x + 1x2 + 405 + -4x + -1x2 Reorder the terms: 405 + -4x + -1x2 = -405 + 405 + 4x + -4x + 1x2 + -1x2 Combine like terms: -405 + 405 = 0 405 + -4x + -1x2 = 0 + 4x + -4x + 1x2 + -1x2 405 + -4x + -1x2 = 4x + -4x + 1x2 + -1x2 Combine like terms: 4x + -4x = 0 405 + -4x + -1x2 = 0 + 1x2 + -1x2 405 + -4x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 405 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -405 + 4x + x2 = 0 Move the constant term to the right: Add '405' to each side of the equation. -405 + 4x + 405 + x2 = 0 + 405 Reorder the terms: -405 + 405 + 4x + x2 = 0 + 405 Combine like terms: -405 + 405 = 0 0 + 4x + x2 = 0 + 405 4x + x2 = 0 + 405 Combine like terms: 0 + 405 = 405 4x + x2 = 405 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 405 + 4 Reorder the terms: 4 + 4x + x2 = 405 + 4 Combine like terms: 405 + 4 = 409 4 + 4x + x2 = 409 Factor a perfect square on the left side: (x + 2)(x + 2) = 409 Calculate the square root of the right side: 20.223748416 Break this problem into two subproblems by setting (x + 2) equal to 20.223748416 and -20.223748416.Subproblem 1
x + 2 = 20.223748416 Simplifying x + 2 = 20.223748416 Reorder the terms: 2 + x = 20.223748416 Solving 2 + x = 20.223748416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 20.223748416 + -2 Combine like terms: 2 + -2 = 0 0 + x = 20.223748416 + -2 x = 20.223748416 + -2 Combine like terms: 20.223748416 + -2 = 18.223748416 x = 18.223748416 Simplifying x = 18.223748416Subproblem 2
x + 2 = -20.223748416 Simplifying x + 2 = -20.223748416 Reorder the terms: 2 + x = -20.223748416 Solving 2 + x = -20.223748416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -20.223748416 + -2 Combine like terms: 2 + -2 = 0 0 + x = -20.223748416 + -2 x = -20.223748416 + -2 Combine like terms: -20.223748416 + -2 = -22.223748416 x = -22.223748416 Simplifying x = -22.223748416Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.223748416, -22.223748416}
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