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Simplifying x2 + -8x + -65 = 10 Reorder the terms: -65 + -8x + x2 = 10 Solving -65 + -8x + x2 = 10 Solving for variable 'x'. Reorder the terms: -65 + -10 + -8x + x2 = 10 + -10 Combine like terms: -65 + -10 = -75 -75 + -8x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -75 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + -8x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + -8x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -8x + x2 = 0 + 75 -8x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 -8x + x2 = 75 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 75 + 16 Reorder the terms: 16 + -8x + x2 = 75 + 16 Combine like terms: 75 + 16 = 91 16 + -8x + x2 = 91 Factor a perfect square on the left side: (x + -4)(x + -4) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (x + -4) equal to 9.539392014 and -9.539392014.Subproblem 1
x + -4 = 9.539392014 Simplifying x + -4 = 9.539392014 Reorder the terms: -4 + x = 9.539392014 Solving -4 + x = 9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 9.539392014 + 4 Combine like terms: -4 + 4 = 0 0 + x = 9.539392014 + 4 x = 9.539392014 + 4 Combine like terms: 9.539392014 + 4 = 13.539392014 x = 13.539392014 Simplifying x = 13.539392014Subproblem 2
x + -4 = -9.539392014 Simplifying x + -4 = -9.539392014 Reorder the terms: -4 + x = -9.539392014 Solving -4 + x = -9.539392014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -9.539392014 + 4 Combine like terms: -4 + 4 = 0 0 + x = -9.539392014 + 4 x = -9.539392014 + 4 Combine like terms: -9.539392014 + 4 = -5.539392014 x = -5.539392014 Simplifying x = -5.539392014Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.539392014, -5.539392014}
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