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Simplifying x2 + -6x + -68 = 7 Reorder the terms: -68 + -6x + x2 = 7 Solving -68 + -6x + x2 = 7 Solving for variable 'x'. Reorder the terms: -68 + -7 + -6x + x2 = 7 + -7 Combine like terms: -68 + -7 = -75 -75 + -6x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -75 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + -6x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + -6x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -6x + x2 = 0 + 75 -6x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 -6x + x2 = 75 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 = 75 + 9 Reorder the terms: 9 + -6x + x2 = 75 + 9 Combine like terms: 75 + 9 = 84 9 + -6x + x2 = 84 Factor a perfect square on the left side: (x + -3)(x + -3) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + -3) equal to 9.16515139 and -9.16515139.Subproblem 1
x + -3 = 9.16515139 Simplifying x + -3 = 9.16515139 Reorder the terms: -3 + x = 9.16515139 Solving -3 + x = 9.16515139 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 = 9.16515139 + 3 Combine like terms: -3 + 3 = 0 0 + x = 9.16515139 + 3 x = 9.16515139 + 3 Combine like terms: 9.16515139 + 3 = 12.16515139 x = 12.16515139 Simplifying x = 12.16515139Subproblem 2
x + -3 = -9.16515139 Simplifying x + -3 = -9.16515139 Reorder the terms: -3 + x = -9.16515139 Solving -3 + x = -9.16515139 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 = -9.16515139 + 3 Combine like terms: -3 + 3 = 0 0 + x = -9.16515139 + 3 x = -9.16515139 + 3 Combine like terms: -9.16515139 + 3 = -6.16515139 x = -6.16515139 Simplifying x = -6.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.16515139, -6.16515139}
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