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Simplifying X2 + 6X = 34 Reorder the terms: 6X + X2 = 34 Solving 6X + X2 = 34 Solving for variable 'X'. Reorder the terms: -34 + 6X + X2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + 6X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 6X + 34 + X2 = 0 + 34 Reorder the terms: -34 + 34 + 6X + X2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 6X + X2 = 0 + 34 6X + X2 = 0 + 34 Combine like terms: 0 + 34 = 34 6X + X2 = 34 The X term is 6X. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6X + 9 + X2 = 34 + 9 Reorder the terms: 9 + 6X + X2 = 34 + 9 Combine like terms: 34 + 9 = 43 9 + 6X + X2 = 43 Factor a perfect square on the left side: (X + 3)(X + 3) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (X + 3) equal to 6.557438524 and -6.557438524.Subproblem 1
X + 3 = 6.557438524 Simplifying X + 3 = 6.557438524 Reorder the terms: 3 + X = 6.557438524 Solving 3 + X = 6.557438524 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = 6.557438524 + -3 Combine like terms: 3 + -3 = 0 0 + X = 6.557438524 + -3 X = 6.557438524 + -3 Combine like terms: 6.557438524 + -3 = 3.557438524 X = 3.557438524 Simplifying X = 3.557438524Subproblem 2
X + 3 = -6.557438524 Simplifying X + 3 = -6.557438524 Reorder the terms: 3 + X = -6.557438524 Solving 3 + X = -6.557438524 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + X = -6.557438524 + -3 Combine like terms: 3 + -3 = 0 0 + X = -6.557438524 + -3 X = -6.557438524 + -3 Combine like terms: -6.557438524 + -3 = -9.557438524 X = -9.557438524 Simplifying X = -9.557438524Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.557438524, -9.557438524}
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