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Simplifying x2 + -8x + 64 = 76.5 Reorder the terms: 64 + -8x + x2 = 76.5 Solving 64 + -8x + x2 = 76.5 Solving for variable 'x'. Reorder the terms: 64 + -76.5 + -8x + x2 = 76.5 + -76.5 Combine like terms: 64 + -76.5 = -12.5 -12.5 + -8x + x2 = 76.5 + -76.5 Combine like terms: 76.5 + -76.5 = 0.0 -12.5 + -8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -8x + 12.5 + x2 = 0.0 + 12.5 Reorder the terms: -12.5 + 12.5 + -8x + x2 = 0.0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -8x + x2 = 0.0 + 12.5 -8x + x2 = 0.0 + 12.5 Combine like terms: 0.0 + 12.5 = 12.5 -8x + x2 = 12.5 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 = 12.5 + 16 Reorder the terms: 16 + -8x + x2 = 12.5 + 16 Combine like terms: 12.5 + 16 = 28.5 16 + -8x + x2 = 28.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 28.5 Calculate the square root of the right side: 5.338539126 Break this problem into two subproblems by setting (x + -4) equal to 5.338539126 and -5.338539126.Subproblem 1
x + -4 = 5.338539126 Simplifying x + -4 = 5.338539126 Reorder the terms: -4 + x = 5.338539126 Solving -4 + x = 5.338539126 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 = 5.338539126 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.338539126 + 4 x = 5.338539126 + 4 Combine like terms: 5.338539126 + 4 = 9.338539126 x = 9.338539126 Simplifying x = 9.338539126Subproblem 2
x + -4 = -5.338539126 Simplifying x + -4 = -5.338539126 Reorder the terms: -4 + x = -5.338539126 Solving -4 + x = -5.338539126 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 = -5.338539126 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.338539126 + 4 x = -5.338539126 + 4 Combine like terms: -5.338539126 + 4 = -1.338539126 x = -1.338539126 Simplifying x = -1.338539126Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.338539126, -1.338539126}
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