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Simplifying 100x2 + -245x + -600 = 0 Reorder the terms: -600 + -245x + 100x2 = 0 Solving -600 + -245x + 100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-120 + -49x + 20x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-120 + -49x + 20x2)' equal to zero and attempt to solve: Simplifying -120 + -49x + 20x2 = 0 Solving -120 + -49x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -6 + -2.45x + x2 = 0.0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2.45x + 6 + x2 = 0.0 + 6 Reorder the terms: -6 + 6 + -2.45x + x2 = 0.0 + 6 Combine like terms: -6 + 6 = 0 0 + -2.45x + x2 = 0.0 + 6 -2.45x + x2 = 0.0 + 6 Combine like terms: 0.0 + 6 = 6 -2.45x + x2 = 6 The x term is -2.45x. Take half its coefficient (-1.225). Square it (1.500625) and add it to both sides. Add '1.500625' to each side of the equation. -2.45x + 1.500625 + x2 = 6 + 1.500625 Reorder the terms: 1.500625 + -2.45x + x2 = 6 + 1.500625 Combine like terms: 6 + 1.500625 = 7.500625 1.500625 + -2.45x + x2 = 7.500625 Factor a perfect square on the left side: (x + -1.225)(x + -1.225) = 7.500625 Calculate the square root of the right side: 2.738726894 Break this problem into two subproblems by setting (x + -1.225) equal to 2.738726894 and -2.738726894.Subproblem 1
x + -1.225 = 2.738726894 Simplifying x + -1.225 = 2.738726894 Reorder the terms: -1.225 + x = 2.738726894 Solving -1.225 + x = 2.738726894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.225' to each side of the equation. -1.225 + 1.225 + x = 2.738726894 + 1.225 Combine like terms: -1.225 + 1.225 = 0.000 0.000 + x = 2.738726894 + 1.225 x = 2.738726894 + 1.225 Combine like terms: 2.738726894 + 1.225 = 3.963726894 x = 3.963726894 Simplifying x = 3.963726894Subproblem 2
x + -1.225 = -2.738726894 Simplifying x + -1.225 = -2.738726894 Reorder the terms: -1.225 + x = -2.738726894 Solving -1.225 + x = -2.738726894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.225' to each side of the equation. -1.225 + 1.225 + x = -2.738726894 + 1.225 Combine like terms: -1.225 + 1.225 = 0.000 0.000 + x = -2.738726894 + 1.225 x = -2.738726894 + 1.225 Combine like terms: -2.738726894 + 1.225 = -1.513726894 x = -1.513726894 Simplifying x = -1.513726894Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.963726894, -1.513726894}Solution
x = {3.963726894, -1.513726894}
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