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Simplifying x2 + -8x = 0.95 Reorder the terms: -8x + x2 = 0.95 Solving -8x + x2 = 0.95 Solving for variable 'x'. Reorder the terms: -0.95 + -8x + x2 = 0.95 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 -0.95 + -8x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.95' to each side of the equation. -0.95 + -8x + 0.95 + x2 = 0.00 + 0.95 Reorder the terms: -0.95 + 0.95 + -8x + x2 = 0.00 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + -8x + x2 = 0.00 + 0.95 -8x + x2 = 0.00 + 0.95 Combine like terms: 0.00 + 0.95 = 0.95 -8x + x2 = 0.95 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 = 0.95 + 16 Reorder the terms: 16 + -8x + x2 = 0.95 + 16 Combine like terms: 0.95 + 16 = 16.95 16 + -8x + x2 = 16.95 Factor a perfect square on the left side: (x + -4)(x + -4) = 16.95 Calculate the square root of the right side: 4.11703777 Break this problem into two subproblems by setting (x + -4) equal to 4.11703777 and -4.11703777.Subproblem 1
x + -4 = 4.11703777 Simplifying x + -4 = 4.11703777 Reorder the terms: -4 + x = 4.11703777 Solving -4 + x = 4.11703777 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 = 4.11703777 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.11703777 + 4 x = 4.11703777 + 4 Combine like terms: 4.11703777 + 4 = 8.11703777 x = 8.11703777 Simplifying x = 8.11703777Subproblem 2
x + -4 = -4.11703777 Simplifying x + -4 = -4.11703777 Reorder the terms: -4 + x = -4.11703777 Solving -4 + x = -4.11703777 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 = -4.11703777 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.11703777 + 4 x = -4.11703777 + 4 Combine like terms: -4.11703777 + 4 = -0.11703777 x = -0.11703777 Simplifying x = -0.11703777Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.11703777, -0.11703777}
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