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Simplifying x2 + -8x + 16 = 65 Reorder the terms: 16 + -8x + x2 = 65 Solving 16 + -8x + x2 = 65 Solving for variable 'x'. Reorder the terms: 16 + -65 + -8x + x2 = 65 + -65 Combine like terms: 16 + -65 = -49 -49 + -8x + x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -49 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -8x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -8x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -8x + x2 = 0 + 49 -8x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -8x + x2 = 49 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 = 49 + 16 Reorder the terms: 16 + -8x + x2 = 49 + 16 Combine like terms: 49 + 16 = 65 16 + -8x + x2 = 65 Factor a perfect square on the left side: (x + -4)(x + -4) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + -4) equal to 8.062257748 and -8.062257748.Subproblem 1
x + -4 = 8.062257748 Simplifying x + -4 = 8.062257748 Reorder the terms: -4 + x = 8.062257748 Solving -4 + x = 8.062257748 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 = 8.062257748 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.062257748 + 4 x = 8.062257748 + 4 Combine like terms: 8.062257748 + 4 = 12.062257748 x = 12.062257748 Simplifying x = 12.062257748Subproblem 2
x + -4 = -8.062257748 Simplifying x + -4 = -8.062257748 Reorder the terms: -4 + x = -8.062257748 Solving -4 + x = -8.062257748 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 = -8.062257748 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.062257748 + 4 x = -8.062257748 + 4 Combine like terms: -8.062257748 + 4 = -4.062257748 x = -4.062257748 Simplifying x = -4.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.062257748, -4.062257748}
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