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Simplifying x + x2 + x + -80 = 420 Reorder the terms: -80 + x + x + x2 = 420 Combine like terms: x + x = 2x -80 + 2x + x2 = 420 Solving -80 + 2x + x2 = 420 Solving for variable 'x'. Reorder the terms: -80 + -420 + 2x + x2 = 420 + -420 Combine like terms: -80 + -420 = -500 -500 + 2x + x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -500 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + 2x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 2x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 2x + x2 = 0 + 500 2x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 2x + x2 = 500 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 = 500 + 1 Reorder the terms: 1 + 2x + x2 = 500 + 1 Combine like terms: 500 + 1 = 501 1 + 2x + x2 = 501 Factor a perfect square on the left side: (x + 1)(x + 1) = 501 Calculate the square root of the right side: 22.383029286 Break this problem into two subproblems by setting (x + 1) equal to 22.383029286 and -22.383029286.Subproblem 1
x + 1 = 22.383029286 Simplifying x + 1 = 22.383029286 Reorder the terms: 1 + x = 22.383029286 Solving 1 + x = 22.383029286 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 = 22.383029286 + -1 Combine like terms: 1 + -1 = 0 0 + x = 22.383029286 + -1 x = 22.383029286 + -1 Combine like terms: 22.383029286 + -1 = 21.383029286 x = 21.383029286 Simplifying x = 21.383029286Subproblem 2
x + 1 = -22.383029286 Simplifying x + 1 = -22.383029286 Reorder the terms: 1 + x = -22.383029286 Solving 1 + x = -22.383029286 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 = -22.383029286 + -1 Combine like terms: 1 + -1 = 0 0 + x = -22.383029286 + -1 x = -22.383029286 + -1 Combine like terms: -22.383029286 + -1 = -23.383029286 x = -23.383029286 Simplifying x = -23.383029286Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.383029286, -23.383029286}
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