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Simplifying x2 + 190x = 11 Reorder the terms: 190x + x2 = 11 Solving 190x + x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 190x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 190x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 190x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 190x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 190x + x2 = 0 + 11 190x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 190x + x2 = 11 The x term is 190x. Take half its coefficient (95). Square it (9025) and add it to both sides. Add '9025' to each side of the equation. 190x + 9025 + x2 = 11 + 9025 Reorder the terms: 9025 + 190x + x2 = 11 + 9025 Combine like terms: 11 + 9025 = 9036 9025 + 190x + x2 = 9036 Factor a perfect square on the left side: (x + 95)(x + 95) = 9036 Calculate the square root of the right side: 95.057877107 Break this problem into two subproblems by setting (x + 95) equal to 95.057877107 and -95.057877107.Subproblem 1
x + 95 = 95.057877107 Simplifying x + 95 = 95.057877107 Reorder the terms: 95 + x = 95.057877107 Solving 95 + x = 95.057877107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-95' to each side of the equation. 95 + -95 + x = 95.057877107 + -95 Combine like terms: 95 + -95 = 0 0 + x = 95.057877107 + -95 x = 95.057877107 + -95 Combine like terms: 95.057877107 + -95 = 0.057877107 x = 0.057877107 Simplifying x = 0.057877107Subproblem 2
x + 95 = -95.057877107 Simplifying x + 95 = -95.057877107 Reorder the terms: 95 + x = -95.057877107 Solving 95 + x = -95.057877107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-95' to each side of the equation. 95 + -95 + x = -95.057877107 + -95 Combine like terms: 95 + -95 = 0 0 + x = -95.057877107 + -95 x = -95.057877107 + -95 Combine like terms: -95.057877107 + -95 = -190.057877107 x = -190.057877107 Simplifying x = -190.057877107Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.057877107, -190.057877107}
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