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Simplifying 0 = x2 + 8x + 0.64 Reorder the terms: 0 = 0.64 + 8x + x2 Solving 0 = 0.64 + 8x + x2 Solving for variable 'x'. Combine like terms: 0 + -0.64 = -0.64 -0.64 + -8x + -1x2 = 0.64 + 8x + x2 + -0.64 + -8x + -1x2 Reorder the terms: -0.64 + -8x + -1x2 = 0.64 + -0.64 + 8x + -8x + x2 + -1x2 Combine like terms: 0.64 + -0.64 = 0.00 -0.64 + -8x + -1x2 = 0.00 + 8x + -8x + x2 + -1x2 -0.64 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -0.64 + -8x + -1x2 = 0 + x2 + -1x2 -0.64 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -0.64 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.64 + 8x + x2 = 0 Move the constant term to the right: Add '-0.64' to each side of the equation. 0.64 + 8x + -0.64 + x2 = 0 + -0.64 Reorder the terms: 0.64 + -0.64 + 8x + x2 = 0 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + 8x + x2 = 0 + -0.64 8x + x2 = 0 + -0.64 Combine like terms: 0 + -0.64 = -0.64 8x + x2 = -0.64 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 = -0.64 + 16 Reorder the terms: 16 + 8x + x2 = -0.64 + 16 Combine like terms: -0.64 + 16 = 15.36 16 + 8x + x2 = 15.36 Factor a perfect square on the left side: (x + 4)(x + 4) = 15.36 Calculate the square root of the right side: 3.919183588 Break this problem into two subproblems by setting (x + 4) equal to 3.919183588 and -3.919183588.Subproblem 1
x + 4 = 3.919183588 Simplifying x + 4 = 3.919183588 Reorder the terms: 4 + x = 3.919183588 Solving 4 + x = 3.919183588 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 = 3.919183588 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.919183588 + -4 x = 3.919183588 + -4 Combine like terms: 3.919183588 + -4 = -0.080816412 x = -0.080816412 Simplifying x = -0.080816412Subproblem 2
x + 4 = -3.919183588 Simplifying x + 4 = -3.919183588 Reorder the terms: 4 + x = -3.919183588 Solving 4 + x = -3.919183588 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 = -3.919183588 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.919183588 + -4 x = -3.919183588 + -4 Combine like terms: -3.919183588 + -4 = -7.919183588 x = -7.919183588 Simplifying x = -7.919183588Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.080816412, -7.919183588}
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