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Simplifying x2 + -16x = 0.35 Reorder the terms: -16x + x2 = 0.35 Solving -16x + x2 = 0.35 Solving for variable 'x'. Reorder the terms: -0.35 + -16x + x2 = 0.35 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 -0.35 + -16x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + -16x + 0.35 + x2 = 0.00 + 0.35 Reorder the terms: -0.35 + 0.35 + -16x + x2 = 0.00 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + -16x + x2 = 0.00 + 0.35 -16x + x2 = 0.00 + 0.35 Combine like terms: 0.00 + 0.35 = 0.35 -16x + x2 = 0.35 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 0.35 + 64 Reorder the terms: 64 + -16x + x2 = 0.35 + 64 Combine like terms: 0.35 + 64 = 64.35 64 + -16x + x2 = 64.35 Factor a perfect square on the left side: (x + -8)(x + -8) = 64.35 Calculate the square root of the right side: 8.021845174 Break this problem into two subproblems by setting (x + -8) equal to 8.021845174 and -8.021845174.Subproblem 1
x + -8 = 8.021845174 Simplifying x + -8 = 8.021845174 Reorder the terms: -8 + x = 8.021845174 Solving -8 + x = 8.021845174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 8.021845174 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.021845174 + 8 x = 8.021845174 + 8 Combine like terms: 8.021845174 + 8 = 16.021845174 x = 16.021845174 Simplifying x = 16.021845174Subproblem 2
x + -8 = -8.021845174 Simplifying x + -8 = -8.021845174 Reorder the terms: -8 + x = -8.021845174 Solving -8 + x = -8.021845174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -8.021845174 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.021845174 + 8 x = -8.021845174 + 8 Combine like terms: -8.021845174 + 8 = -0.021845174 x = -0.021845174 Simplifying x = -0.021845174Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.021845174, -0.021845174}
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