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Simplifying x2 + 6x + -829 = 0 Reorder the terms: -829 + 6x + x2 = 0 Solving -829 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '829' to each side of the equation. -829 + 6x + 829 + x2 = 0 + 829 Reorder the terms: -829 + 829 + 6x + x2 = 0 + 829 Combine like terms: -829 + 829 = 0 0 + 6x + x2 = 0 + 829 6x + x2 = 0 + 829 Combine like terms: 0 + 829 = 829 6x + x2 = 829 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 = 829 + 9 Reorder the terms: 9 + 6x + x2 = 829 + 9 Combine like terms: 829 + 9 = 838 9 + 6x + x2 = 838 Factor a perfect square on the left side: (x + 3)(x + 3) = 838 Calculate the square root of the right side: 28.948229652 Break this problem into two subproblems by setting (x + 3) equal to 28.948229652 and -28.948229652.Subproblem 1
x + 3 = 28.948229652 Simplifying x + 3 = 28.948229652 Reorder the terms: 3 + x = 28.948229652 Solving 3 + x = 28.948229652 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 = 28.948229652 + -3 Combine like terms: 3 + -3 = 0 0 + x = 28.948229652 + -3 x = 28.948229652 + -3 Combine like terms: 28.948229652 + -3 = 25.948229652 x = 25.948229652 Simplifying x = 25.948229652Subproblem 2
x + 3 = -28.948229652 Simplifying x + 3 = -28.948229652 Reorder the terms: 3 + x = -28.948229652 Solving 3 + x = -28.948229652 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 = -28.948229652 + -3 Combine like terms: 3 + -3 = 0 0 + x = -28.948229652 + -3 x = -28.948229652 + -3 Combine like terms: -28.948229652 + -3 = -31.948229652 x = -31.948229652 Simplifying x = -31.948229652Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.948229652, -31.948229652}
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