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Simplifying x2 + -6x + -76 = 0 Reorder the terms: -76 + -6x + x2 = 0 Solving -76 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + -6x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + -6x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + -6x + x2 = 0 + 76 -6x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 -6x + x2 = 76 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 = 76 + 9 Reorder the terms: 9 + -6x + x2 = 76 + 9 Combine like terms: 76 + 9 = 85 9 + -6x + x2 = 85 Factor a perfect square on the left side: (x + -3)(x + -3) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x + -3) equal to 9.219544457 and -9.219544457.Subproblem 1
x + -3 = 9.219544457 Simplifying x + -3 = 9.219544457 Reorder the terms: -3 + x = 9.219544457 Solving -3 + x = 9.219544457 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 = 9.219544457 + 3 Combine like terms: -3 + 3 = 0 0 + x = 9.219544457 + 3 x = 9.219544457 + 3 Combine like terms: 9.219544457 + 3 = 12.219544457 x = 12.219544457 Simplifying x = 12.219544457Subproblem 2
x + -3 = -9.219544457 Simplifying x + -3 = -9.219544457 Reorder the terms: -3 + x = -9.219544457 Solving -3 + x = -9.219544457 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 = -9.219544457 + 3 Combine like terms: -3 + 3 = 0 0 + x = -9.219544457 + 3 x = -9.219544457 + 3 Combine like terms: -9.219544457 + 3 = -6.219544457 x = -6.219544457 Simplifying x = -6.219544457Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.219544457, -6.219544457}
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