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Simplifying (x + 8)(x + 8) = 16 + -1x2 + -9x Reorder the terms: (8 + x)(x + 8) = 16 + -1x2 + -9x Reorder the terms: (8 + x)(8 + x) = 16 + -1x2 + -9x Multiply (8 + x) * (8 + x) (8(8 + x) + x(8 + x)) = 16 + -1x2 + -9x ((8 * 8 + x * 8) + x(8 + x)) = 16 + -1x2 + -9x ((64 + 8x) + x(8 + x)) = 16 + -1x2 + -9x (64 + 8x + (8 * x + x * x)) = 16 + -1x2 + -9x (64 + 8x + (8x + x2)) = 16 + -1x2 + -9x Combine like terms: 8x + 8x = 16x (64 + 16x + x2) = 16 + -1x2 + -9x Reorder the terms: 64 + 16x + x2 = 16 + -9x + -1x2 Solving 64 + 16x + x2 = 16 + -9x + -1x2 Solving for variable 'x'. Reorder the terms: 64 + -16 + 16x + 9x + x2 + x2 = 16 + -9x + -1x2 + -16 + 9x + x2 Combine like terms: 64 + -16 = 48 48 + 16x + 9x + x2 + x2 = 16 + -9x + -1x2 + -16 + 9x + x2 Combine like terms: 16x + 9x = 25x 48 + 25x + x2 + x2 = 16 + -9x + -1x2 + -16 + 9x + x2 Combine like terms: x2 + x2 = 2x2 48 + 25x + 2x2 = 16 + -9x + -1x2 + -16 + 9x + x2 Reorder the terms: 48 + 25x + 2x2 = 16 + -16 + -9x + 9x + -1x2 + x2 Combine like terms: 16 + -16 = 0 48 + 25x + 2x2 = 0 + -9x + 9x + -1x2 + x2 48 + 25x + 2x2 = -9x + 9x + -1x2 + x2 Combine like terms: -9x + 9x = 0 48 + 25x + 2x2 = 0 + -1x2 + x2 48 + 25x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 48 + 25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 24 + 12.5x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + 12.5x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 12.5x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 12.5x + x2 = 0 + -24 12.5x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 12.5x + x2 = -24 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = -24 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = -24 + 39.0625 Combine like terms: -24 + 39.0625 = 15.0625 39.0625 + 12.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + 6.25) equal to 3.881043674 and -3.881043674.Subproblem 1
x + 6.25 = 3.881043674 Simplifying x + 6.25 = 3.881043674 Reorder the terms: 6.25 + x = 3.881043674 Solving 6.25 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 3.881043674 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 3.881043674 + -6.25 x = 3.881043674 + -6.25 Combine like terms: 3.881043674 + -6.25 = -2.368956326 x = -2.368956326 Simplifying x = -2.368956326Subproblem 2
x + 6.25 = -3.881043674 Simplifying x + 6.25 = -3.881043674 Reorder the terms: 6.25 + x = -3.881043674 Solving 6.25 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -3.881043674 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -3.881043674 + -6.25 x = -3.881043674 + -6.25 Combine like terms: -3.881043674 + -6.25 = -10.131043674 x = -10.131043674 Simplifying x = -10.131043674Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.368956326, -10.131043674}
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