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Simplifying x + x + -40 + x * x = 420 Multiply x * x x + x + -40 + x2 = 420 Reorder the terms: -40 + x + x + x2 = 420 Combine like terms: x + x = 2x -40 + 2x + x2 = 420 Solving -40 + 2x + x2 = 420 Solving for variable 'x'. Reorder the terms: -40 + -420 + 2x + x2 = 420 + -420 Combine like terms: -40 + -420 = -460 -460 + 2x + x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -460 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '460' to each side of the equation. -460 + 2x + 460 + x2 = 0 + 460 Reorder the terms: -460 + 460 + 2x + x2 = 0 + 460 Combine like terms: -460 + 460 = 0 0 + 2x + x2 = 0 + 460 2x + x2 = 0 + 460 Combine like terms: 0 + 460 = 460 2x + x2 = 460 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 = 460 + 1 Reorder the terms: 1 + 2x + x2 = 460 + 1 Combine like terms: 460 + 1 = 461 1 + 2x + x2 = 461 Factor a perfect square on the left side: (x + 1)(x + 1) = 461 Calculate the square root of the right side: 21.470910554 Break this problem into two subproblems by setting (x + 1) equal to 21.470910554 and -21.470910554.Subproblem 1
x + 1 = 21.470910554 Simplifying x + 1 = 21.470910554 Reorder the terms: 1 + x = 21.470910554 Solving 1 + x = 21.470910554 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 = 21.470910554 + -1 Combine like terms: 1 + -1 = 0 0 + x = 21.470910554 + -1 x = 21.470910554 + -1 Combine like terms: 21.470910554 + -1 = 20.470910554 x = 20.470910554 Simplifying x = 20.470910554Subproblem 2
x + 1 = -21.470910554 Simplifying x + 1 = -21.470910554 Reorder the terms: 1 + x = -21.470910554 Solving 1 + x = -21.470910554 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 = -21.470910554 + -1 Combine like terms: 1 + -1 = 0 0 + x = -21.470910554 + -1 x = -21.470910554 + -1 Combine like terms: -21.470910554 + -1 = -22.470910554 x = -22.470910554 Simplifying x = -22.470910554Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.470910554, -22.470910554}
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