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Simplifying x(x + 8) = 4.65 Reorder the terms: x(8 + x) = 4.65 (8 * x + x * x) = 4.65 (8x + x2) = 4.65 Solving 8x + x2 = 4.65 Solving for variable 'x'. Reorder the terms: -4.65 + 8x + x2 = 4.65 + -4.65 Combine like terms: 4.65 + -4.65 = 0.00 -4.65 + 8x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '4.65' to each side of the equation. -4.65 + 8x + 4.65 + x2 = 0.00 + 4.65 Reorder the terms: -4.65 + 4.65 + 8x + x2 = 0.00 + 4.65 Combine like terms: -4.65 + 4.65 = 0.00 0.00 + 8x + x2 = 0.00 + 4.65 8x + x2 = 0.00 + 4.65 Combine like terms: 0.00 + 4.65 = 4.65 8x + x2 = 4.65 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 = 4.65 + 16 Reorder the terms: 16 + 8x + x2 = 4.65 + 16 Combine like terms: 4.65 + 16 = 20.65 16 + 8x + x2 = 20.65 Factor a perfect square on the left side: (x + 4)(x + 4) = 20.65 Calculate the square root of the right side: 4.544227107 Break this problem into two subproblems by setting (x + 4) equal to 4.544227107 and -4.544227107.Subproblem 1
x + 4 = 4.544227107 Simplifying x + 4 = 4.544227107 Reorder the terms: 4 + x = 4.544227107 Solving 4 + x = 4.544227107 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 = 4.544227107 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.544227107 + -4 x = 4.544227107 + -4 Combine like terms: 4.544227107 + -4 = 0.544227107 x = 0.544227107 Simplifying x = 0.544227107Subproblem 2
x + 4 = -4.544227107 Simplifying x + 4 = -4.544227107 Reorder the terms: 4 + x = -4.544227107 Solving 4 + x = -4.544227107 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 = -4.544227107 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.544227107 + -4 x = -4.544227107 + -4 Combine like terms: -4.544227107 + -4 = -8.544227107 x = -8.544227107 Simplifying x = -8.544227107Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.544227107, -8.544227107}
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