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Simplifying x6 + 2x3 = 71 Reorder the terms: 2x3 + x6 = 71 Solving 2x3 + x6 = 71 Solving for variable 'x'. Reorder the terms: -71 + 2x3 + x6 = 71 + -71 Combine like terms: 71 + -71 = 0 -71 + 2x3 + x6 = 0 Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + 2x3 + 71 + x6 = 0 + 71 Reorder the terms: -71 + 71 + 2x3 + x6 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + 2x3 + x6 = 0 + 71 2x3 + x6 = 0 + 71 Combine like terms: 0 + 71 = 71 2x3 + x6 = 71 The x term is 2x3. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x3 + 1 + x6 = 71 + 1 Reorder the terms: 1 + 2x3 + x6 = 71 + 1 Combine like terms: 71 + 1 = 72 1 + 2x3 + x6 = 72 Factor a perfect square on the left side: (x3 + 1)(x3 + 1) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x3 + 1) equal to 8.485281374 and -8.485281374.Subproblem 1
x3 + 1 = 8.485281374 Simplifying x3 + 1 = 8.485281374 Reorder the terms: 1 + x3 = 8.485281374 Solving 1 + x3 = 8.485281374 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 + x3 = 8.485281374 + -1 Combine like terms: 1 + -1 = 0 0 + x3 = 8.485281374 + -1 x3 = 8.485281374 + -1 Combine like terms: 8.485281374 + -1 = 7.485281374 x3 = 7.485281374 Simplifying x3 = 7.485281374 Reorder the terms: -7.485281374 + x3 = 7.485281374 + -7.485281374 Combine like terms: 7.485281374 + -7.485281374 = 0.000000000 -7.485281374 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + 1 = -8.485281374 Simplifying x3 + 1 = -8.485281374 Reorder the terms: 1 + x3 = -8.485281374 Solving 1 + x3 = -8.485281374 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 + x3 = -8.485281374 + -1 Combine like terms: 1 + -1 = 0 0 + x3 = -8.485281374 + -1 x3 = -8.485281374 + -1 Combine like terms: -8.485281374 + -1 = -9.485281374 x3 = -9.485281374 Simplifying x3 = -9.485281374 Reorder the terms: 9.485281374 + x3 = -9.485281374 + 9.485281374 Combine like terms: -9.485281374 + 9.485281374 = 0.000000000 9.485281374 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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