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Simplifying 4000x2 + -49x + -98 = 0 Reorder the terms: -98 + -49x + 4000x2 = 0 Solving -98 + -49x + 4000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4000 the coefficient of the squared term: Divide each side by '4000'. -0.0245 + -0.01225x + x2 = 0 Move the constant term to the right: Add '0.0245' to each side of the equation. -0.0245 + -0.01225x + 0.0245 + x2 = 0 + 0.0245 Reorder the terms: -0.0245 + 0.0245 + -0.01225x + x2 = 0 + 0.0245 Combine like terms: -0.0245 + 0.0245 = 0.0000 0.0000 + -0.01225x + x2 = 0 + 0.0245 -0.01225x + x2 = 0 + 0.0245 Combine like terms: 0 + 0.0245 = 0.0245 -0.01225x + x2 = 0.0245 The x term is -0.01225x. Take half its coefficient (-0.006125). Square it (0.000037515625) and add it to both sides. Add '0.000037515625' to each side of the equation. -0.01225x + 0.000037515625 + x2 = 0.0245 + 0.000037515625 Reorder the terms: 0.000037515625 + -0.01225x + x2 = 0.0245 + 0.000037515625 Combine like terms: 0.0245 + 0.000037515625 = 0.024537515625 0.000037515625 + -0.01225x + x2 = 0.024537515625 Factor a perfect square on the left side: (x + -0.006125)(x + -0.006125) = 0.024537515625 Calculate the square root of the right side: 0.156644552 Break this problem into two subproblems by setting (x + -0.006125) equal to 0.156644552 and -0.156644552.Subproblem 1
x + -0.006125 = 0.156644552 Simplifying x + -0.006125 = 0.156644552 Reorder the terms: -0.006125 + x = 0.156644552 Solving -0.006125 + x = 0.156644552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006125' to each side of the equation. -0.006125 + 0.006125 + x = 0.156644552 + 0.006125 Combine like terms: -0.006125 + 0.006125 = 0.000000 0.000000 + x = 0.156644552 + 0.006125 x = 0.156644552 + 0.006125 Combine like terms: 0.156644552 + 0.006125 = 0.162769552 x = 0.162769552 Simplifying x = 0.162769552Subproblem 2
x + -0.006125 = -0.156644552 Simplifying x + -0.006125 = -0.156644552 Reorder the terms: -0.006125 + x = -0.156644552 Solving -0.006125 + x = -0.156644552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006125' to each side of the equation. -0.006125 + 0.006125 + x = -0.156644552 + 0.006125 Combine like terms: -0.006125 + 0.006125 = 0.000000 0.000000 + x = -0.156644552 + 0.006125 x = -0.156644552 + 0.006125 Combine like terms: -0.156644552 + 0.006125 = -0.150519552 x = -0.150519552 Simplifying x = -0.150519552Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.162769552, -0.150519552}
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