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Simplifying 0 = x2 + -2x + -405 Reorder the terms: 0 = -405 + -2x + x2 Solving 0 = -405 + -2x + x2 Solving for variable 'x'. Combine like terms: 0 + 405 = 405 405 + 2x + -1x2 = -405 + -2x + x2 + 405 + 2x + -1x2 Reorder the terms: 405 + 2x + -1x2 = -405 + 405 + -2x + 2x + x2 + -1x2 Combine like terms: -405 + 405 = 0 405 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2 405 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 405 + 2x + -1x2 = 0 + x2 + -1x2 405 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 405 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -405 + -2x + x2 = 0 Move the constant term to the right: Add '405' to each side of the equation. -405 + -2x + 405 + x2 = 0 + 405 Reorder the terms: -405 + 405 + -2x + x2 = 0 + 405 Combine like terms: -405 + 405 = 0 0 + -2x + x2 = 0 + 405 -2x + x2 = 0 + 405 Combine like terms: 0 + 405 = 405 -2x + x2 = 405 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 405 + 1 Reorder the terms: 1 + -2x + x2 = 405 + 1 Combine like terms: 405 + 1 = 406 1 + -2x + x2 = 406 Factor a perfect square on the left side: (x + -1)(x + -1) = 406 Calculate the square root of the right side: 20.14944168 Break this problem into two subproblems by setting (x + -1) equal to 20.14944168 and -20.14944168.Subproblem 1
x + -1 = 20.14944168 Simplifying x + -1 = 20.14944168 Reorder the terms: -1 + x = 20.14944168 Solving -1 + x = 20.14944168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 20.14944168 + 1 Combine like terms: -1 + 1 = 0 0 + x = 20.14944168 + 1 x = 20.14944168 + 1 Combine like terms: 20.14944168 + 1 = 21.14944168 x = 21.14944168 Simplifying x = 21.14944168Subproblem 2
x + -1 = -20.14944168 Simplifying x + -1 = -20.14944168 Reorder the terms: -1 + x = -20.14944168 Solving -1 + x = -20.14944168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -20.14944168 + 1 Combine like terms: -1 + 1 = 0 0 + x = -20.14944168 + 1 x = -20.14944168 + 1 Combine like terms: -20.14944168 + 1 = -19.14944168 x = -19.14944168 Simplifying x = -19.14944168Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.14944168, -19.14944168}
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