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Simplifying x2 = 42 + 2x Solving x2 = 42 + 2x Solving for variable 'x'. Reorder the terms: -42 + -2x + x2 = 42 + 2x + -42 + -2x Reorder the terms: -42 + -2x + x2 = 42 + -42 + 2x + -2x Combine like terms: 42 + -42 = 0 -42 + -2x + x2 = 0 + 2x + -2x -42 + -2x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -42 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -2x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -2x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -2x + x2 = 0 + 42 -2x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -2x + x2 = 42 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 = 42 + 1 Reorder the terms: 1 + -2x + x2 = 42 + 1 Combine like terms: 42 + 1 = 43 1 + -2x + x2 = 43 Factor a perfect square on the left side: (x + -1)(x + -1) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + -1) equal to 6.557438524 and -6.557438524.Subproblem 1
x + -1 = 6.557438524 Simplifying x + -1 = 6.557438524 Reorder the terms: -1 + x = 6.557438524 Solving -1 + x = 6.557438524 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 = 6.557438524 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.557438524 + 1 x = 6.557438524 + 1 Combine like terms: 6.557438524 + 1 = 7.557438524 x = 7.557438524 Simplifying x = 7.557438524Subproblem 2
x + -1 = -6.557438524 Simplifying x + -1 = -6.557438524 Reorder the terms: -1 + x = -6.557438524 Solving -1 + x = -6.557438524 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 = -6.557438524 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.557438524 + 1 x = -6.557438524 + 1 Combine like terms: -6.557438524 + 1 = -5.557438524 x = -5.557438524 Simplifying x = -5.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.557438524, -5.557438524}
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