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Simplifying 995 = 6x + x2 Solving 995 = 6x + x2 Solving for variable 'x'. Reorder the terms: 995 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 995 + -6x + -1x2 = 0 + x2 + -1x2 995 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 995 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -995 + 6x + x2 = 0 Move the constant term to the right: Add '995' to each side of the equation. -995 + 6x + 995 + x2 = 0 + 995 Reorder the terms: -995 + 995 + 6x + x2 = 0 + 995 Combine like terms: -995 + 995 = 0 0 + 6x + x2 = 0 + 995 6x + x2 = 0 + 995 Combine like terms: 0 + 995 = 995 6x + x2 = 995 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 = 995 + 9 Reorder the terms: 9 + 6x + x2 = 995 + 9 Combine like terms: 995 + 9 = 1004 9 + 6x + x2 = 1004 Factor a perfect square on the left side: (x + 3)(x + 3) = 1004 Calculate the square root of the right side: 31.685959036 Break this problem into two subproblems by setting (x + 3) equal to 31.685959036 and -31.685959036.Subproblem 1
x + 3 = 31.685959036 Simplifying x + 3 = 31.685959036 Reorder the terms: 3 + x = 31.685959036 Solving 3 + x = 31.685959036 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 = 31.685959036 + -3 Combine like terms: 3 + -3 = 0 0 + x = 31.685959036 + -3 x = 31.685959036 + -3 Combine like terms: 31.685959036 + -3 = 28.685959036 x = 28.685959036 Simplifying x = 28.685959036Subproblem 2
x + 3 = -31.685959036 Simplifying x + 3 = -31.685959036 Reorder the terms: 3 + x = -31.685959036 Solving 3 + x = -31.685959036 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 = -31.685959036 + -3 Combine like terms: 3 + -3 = 0 0 + x = -31.685959036 + -3 x = -31.685959036 + -3 Combine like terms: -31.685959036 + -3 = -34.685959036 x = -34.685959036 Simplifying x = -34.685959036Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.685959036, -34.685959036}
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