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Simplifying x2 + -914x + 191.949 = 0 Reorder the terms: 191.949 + -914x + x2 = 0 Solving 191.949 + -914x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-191.949' to each side of the equation. 191.949 + -914x + -191.949 + x2 = 0 + -191.949 Reorder the terms: 191.949 + -191.949 + -914x + x2 = 0 + -191.949 Combine like terms: 191.949 + -191.949 = 0.000 0.000 + -914x + x2 = 0 + -191.949 -914x + x2 = 0 + -191.949 Combine like terms: 0 + -191.949 = -191.949 -914x + x2 = -191.949 The x term is -914x. Take half its coefficient (-457). Square it (208849) and add it to both sides. Add '208849' to each side of the equation. -914x + 208849 + x2 = -191.949 + 208849 Reorder the terms: 208849 + -914x + x2 = -191.949 + 208849 Combine like terms: -191.949 + 208849 = 208657.051 208849 + -914x + x2 = 208657.051 Factor a perfect square on the left side: (x + -457)(x + -457) = 208657.051 Calculate the square root of the right side: 456.789941877 Break this problem into two subproblems by setting (x + -457) equal to 456.789941877 and -456.789941877.Subproblem 1
x + -457 = 456.789941877 Simplifying x + -457 = 456.789941877 Reorder the terms: -457 + x = 456.789941877 Solving -457 + x = 456.789941877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '457' to each side of the equation. -457 + 457 + x = 456.789941877 + 457 Combine like terms: -457 + 457 = 0 0 + x = 456.789941877 + 457 x = 456.789941877 + 457 Combine like terms: 456.789941877 + 457 = 913.789941877 x = 913.789941877 Simplifying x = 913.789941877Subproblem 2
x + -457 = -456.789941877 Simplifying x + -457 = -456.789941877 Reorder the terms: -457 + x = -456.789941877 Solving -457 + x = -456.789941877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '457' to each side of the equation. -457 + 457 + x = -456.789941877 + 457 Combine like terms: -457 + 457 = 0 0 + x = -456.789941877 + 457 x = -456.789941877 + 457 Combine like terms: -456.789941877 + 457 = 0.210058123 x = 0.210058123 Simplifying x = 0.210058123Solution
The solution to the problem is based on the solutions from the subproblems. x = {913.789941877, 0.210058123}
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