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Simplifying 245x2 + -13x + -5 = 0 Reorder the terms: -5 + -13x + 245x2 = 0 Solving -5 + -13x + 245x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 245 the coefficient of the squared term: Divide each side by '245'. -0.02040816327 + -0.05306122449x + x2 = 0 Move the constant term to the right: Add '0.02040816327' to each side of the equation. -0.02040816327 + -0.05306122449x + 0.02040816327 + x2 = 0 + 0.02040816327 Reorder the terms: -0.02040816327 + 0.02040816327 + -0.05306122449x + x2 = 0 + 0.02040816327 Combine like terms: -0.02040816327 + 0.02040816327 = 0.00000000000 0.00000000000 + -0.05306122449x + x2 = 0 + 0.02040816327 -0.05306122449x + x2 = 0 + 0.02040816327 Combine like terms: 0 + 0.02040816327 = 0.02040816327 -0.05306122449x + x2 = 0.02040816327 The x term is -0.05306122449x. Take half its coefficient (-0.02653061225). Square it (0.0007038733864) and add it to both sides. Add '0.0007038733864' to each side of the equation. -0.05306122449x + 0.0007038733864 + x2 = 0.02040816327 + 0.0007038733864 Reorder the terms: 0.0007038733864 + -0.05306122449x + x2 = 0.02040816327 + 0.0007038733864 Combine like terms: 0.02040816327 + 0.0007038733864 = 0.0211120366564 0.0007038733864 + -0.05306122449x + x2 = 0.0211120366564 Factor a perfect square on the left side: (x + -0.02653061225)(x + -0.02653061225) = 0.0211120366564 Calculate the square root of the right side: 0.145299816 Break this problem into two subproblems by setting (x + -0.02653061225) equal to 0.145299816 and -0.145299816.Subproblem 1
x + -0.02653061225 = 0.145299816 Simplifying x + -0.02653061225 = 0.145299816 Reorder the terms: -0.02653061225 + x = 0.145299816 Solving -0.02653061225 + x = 0.145299816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02653061225' to each side of the equation. -0.02653061225 + 0.02653061225 + x = 0.145299816 + 0.02653061225 Combine like terms: -0.02653061225 + 0.02653061225 = 0.00000000000 0.00000000000 + x = 0.145299816 + 0.02653061225 x = 0.145299816 + 0.02653061225 Combine like terms: 0.145299816 + 0.02653061225 = 0.17183042825 x = 0.17183042825 Simplifying x = 0.17183042825Subproblem 2
x + -0.02653061225 = -0.145299816 Simplifying x + -0.02653061225 = -0.145299816 Reorder the terms: -0.02653061225 + x = -0.145299816 Solving -0.02653061225 + x = -0.145299816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02653061225' to each side of the equation. -0.02653061225 + 0.02653061225 + x = -0.145299816 + 0.02653061225 Combine like terms: -0.02653061225 + 0.02653061225 = 0.00000000000 0.00000000000 + x = -0.145299816 + 0.02653061225 x = -0.145299816 + 0.02653061225 Combine like terms: -0.145299816 + 0.02653061225 = -0.11876920375 x = -0.11876920375 Simplifying x = -0.11876920375Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.17183042825, -0.11876920375}
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