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Simplifying x2 + 6x + -83 = 3 Reorder the terms: -83 + 6x + x2 = 3 Solving -83 + 6x + x2 = 3 Solving for variable 'x'. Reorder the terms: -83 + -3 + 6x + x2 = 3 + -3 Combine like terms: -83 + -3 = -86 -86 + 6x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -86 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '86' to each side of the equation. -86 + 6x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + 6x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + 6x + x2 = 0 + 86 6x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 6x + x2 = 86 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 = 86 + 9 Reorder the terms: 9 + 6x + x2 = 86 + 9 Combine like terms: 86 + 9 = 95 9 + 6x + x2 = 95 Factor a perfect square on the left side: (x + 3)(x + 3) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (x + 3) equal to 9.746794345 and -9.746794345.Subproblem 1
x + 3 = 9.746794345 Simplifying x + 3 = 9.746794345 Reorder the terms: 3 + x = 9.746794345 Solving 3 + x = 9.746794345 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 = 9.746794345 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.746794345 + -3 x = 9.746794345 + -3 Combine like terms: 9.746794345 + -3 = 6.746794345 x = 6.746794345 Simplifying x = 6.746794345Subproblem 2
x + 3 = -9.746794345 Simplifying x + 3 = -9.746794345 Reorder the terms: 3 + x = -9.746794345 Solving 3 + x = -9.746794345 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 = -9.746794345 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.746794345 + -3 x = -9.746794345 + -3 Combine like terms: -9.746794345 + -3 = -12.746794345 x = -12.746794345 Simplifying x = -12.746794345Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.746794345, -12.746794345}
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