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Simplifying 16x2 + -30x + 1 = 0 Reorder the terms: 1 + -30x + 16x2 = 0 Solving 1 + -30x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -1.875x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -1.875x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -1.875x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -1.875x + x2 = 0 + -0.0625 -1.875x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -1.875x + x2 = -0.0625 The x term is -1.875x. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875x + 0.87890625 + x2 = -0.0625 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = -0.0625 + 0.87890625 Combine like terms: -0.0625 + 0.87890625 = 0.81640625 0.87890625 + -1.875x + x2 = 0.81640625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 0.81640625 Calculate the square root of the right side: 0.903552018 Break this problem into two subproblems by setting (x + -0.9375) equal to 0.903552018 and -0.903552018.Subproblem 1
x + -0.9375 = 0.903552018 Simplifying x + -0.9375 = 0.903552018 Reorder the terms: -0.9375 + x = 0.903552018 Solving -0.9375 + x = 0.903552018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = 0.903552018 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 0.903552018 + 0.9375 x = 0.903552018 + 0.9375 Combine like terms: 0.903552018 + 0.9375 = 1.841052018 x = 1.841052018 Simplifying x = 1.841052018Subproblem 2
x + -0.9375 = -0.903552018 Simplifying x + -0.9375 = -0.903552018 Reorder the terms: -0.9375 + x = -0.903552018 Solving -0.9375 + x = -0.903552018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = -0.903552018 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -0.903552018 + 0.9375 x = -0.903552018 + 0.9375 Combine like terms: -0.903552018 + 0.9375 = 0.033947982 x = 0.033947982 Simplifying x = 0.033947982Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.841052018, 0.033947982}
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