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Simplifying x2 + 8x = 0.2 Reorder the terms: 8x + x2 = 0.2 Solving 8x + x2 = 0.2 Solving for variable 'x'. Reorder the terms: -0.2 + 8x + x2 = 0.2 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 -0.2 + 8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 8x + 0.2 + x2 = 0.0 + 0.2 Reorder the terms: -0.2 + 0.2 + 8x + x2 = 0.0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 8x + x2 = 0.0 + 0.2 8x + x2 = 0.0 + 0.2 Combine like terms: 0.0 + 0.2 = 0.2 8x + x2 = 0.2 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 = 0.2 + 16 Reorder the terms: 16 + 8x + x2 = 0.2 + 16 Combine like terms: 0.2 + 16 = 16.2 16 + 8x + x2 = 16.2 Factor a perfect square on the left side: (x + 4)(x + 4) = 16.2 Calculate the square root of the right side: 4.02492236 Break this problem into two subproblems by setting (x + 4) equal to 4.02492236 and -4.02492236.Subproblem 1
x + 4 = 4.02492236 Simplifying x + 4 = 4.02492236 Reorder the terms: 4 + x = 4.02492236 Solving 4 + x = 4.02492236 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 = 4.02492236 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.02492236 + -4 x = 4.02492236 + -4 Combine like terms: 4.02492236 + -4 = 0.02492236 x = 0.02492236 Simplifying x = 0.02492236Subproblem 2
x + 4 = -4.02492236 Simplifying x + 4 = -4.02492236 Reorder the terms: 4 + x = -4.02492236 Solving 4 + x = -4.02492236 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 = -4.02492236 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.02492236 + -4 x = -4.02492236 + -4 Combine like terms: -4.02492236 + -4 = -8.02492236 x = -8.02492236 Simplifying x = -8.02492236Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.02492236, -8.02492236}
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