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Simplifying 50X2 + -1X + -10 = 0 Reorder the terms: -10 + -1X + 50X2 = 0 Solving -10 + -1X + 50X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.2 + -0.02X + X2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.02X + 0.2 + X2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.02X + X2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.02X + X2 = 0 + 0.2 -0.02X + X2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.02X + X2 = 0.2 The X term is -0.02X. Take half its coefficient (-0.01). Square it (0.0001) and add it to both sides. Add '0.0001' to each side of the equation. -0.02X + 0.0001 + X2 = 0.2 + 0.0001 Reorder the terms: 0.0001 + -0.02X + X2 = 0.2 + 0.0001 Combine like terms: 0.2 + 0.0001 = 0.2001 0.0001 + -0.02X + X2 = 0.2001 Factor a perfect square on the left side: (X + -0.01)(X + -0.01) = 0.2001 Calculate the square root of the right side: 0.447325385 Break this problem into two subproblems by setting (X + -0.01) equal to 0.447325385 and -0.447325385.Subproblem 1
X + -0.01 = 0.447325385 Simplifying X + -0.01 = 0.447325385 Reorder the terms: -0.01 + X = 0.447325385 Solving -0.01 + X = 0.447325385 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.01' to each side of the equation. -0.01 + 0.01 + X = 0.447325385 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + X = 0.447325385 + 0.01 X = 0.447325385 + 0.01 Combine like terms: 0.447325385 + 0.01 = 0.457325385 X = 0.457325385 Simplifying X = 0.457325385Subproblem 2
X + -0.01 = -0.447325385 Simplifying X + -0.01 = -0.447325385 Reorder the terms: -0.01 + X = -0.447325385 Solving -0.01 + X = -0.447325385 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.01' to each side of the equation. -0.01 + 0.01 + X = -0.447325385 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + X = -0.447325385 + 0.01 X = -0.447325385 + 0.01 Combine like terms: -0.447325385 + 0.01 = -0.437325385 X = -0.437325385 Simplifying X = -0.437325385Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.457325385, -0.437325385}
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