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Simplifying 2x + x2 + 3 + 2x + 5 = 84 Reorder the terms: 3 + 5 + 2x + 2x + x2 = 84 Combine like terms: 3 + 5 = 8 8 + 2x + 2x + x2 = 84 Combine like terms: 2x + 2x = 4x 8 + 4x + x2 = 84 Solving 8 + 4x + x2 = 84 Solving for variable 'x'. Reorder the terms: 8 + -84 + 4x + x2 = 84 + -84 Combine like terms: 8 + -84 = -76 -76 + 4x + x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -76 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 4x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + 4x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 4x + x2 = 0 + 76 4x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 4x + x2 = 76 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 = 76 + 4 Reorder the terms: 4 + 4x + x2 = 76 + 4 Combine like terms: 76 + 4 = 80 4 + 4x + x2 = 80 Factor a perfect square on the left side: (x + 2)(x + 2) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + 2) equal to 8.94427191 and -8.94427191.Subproblem 1
x + 2 = 8.94427191 Simplifying x + 2 = 8.94427191 Reorder the terms: 2 + x = 8.94427191 Solving 2 + x = 8.94427191 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 = 8.94427191 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.94427191 + -2 x = 8.94427191 + -2 Combine like terms: 8.94427191 + -2 = 6.94427191 x = 6.94427191 Simplifying x = 6.94427191Subproblem 2
x + 2 = -8.94427191 Simplifying x + 2 = -8.94427191 Reorder the terms: 2 + x = -8.94427191 Solving 2 + x = -8.94427191 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 = -8.94427191 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.94427191 + -2 x = -8.94427191 + -2 Combine like terms: -8.94427191 + -2 = -10.94427191 x = -10.94427191 Simplifying x = -10.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.94427191, -10.94427191}
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