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Simplifying 600x2 + -350x + -275 = 0 Reorder the terms: -275 + -350x + 600x2 = 0 Solving -275 + -350x + 600x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '25'. 25(-11 + -14x + 24x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-11 + -14x + 24x2)' equal to zero and attempt to solve: Simplifying -11 + -14x + 24x2 = 0 Solving -11 + -14x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.4583333333 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '0.4583333333' to each side of the equation. -0.4583333333 + -0.5833333333x + 0.4583333333 + x2 = 0 + 0.4583333333 Reorder the terms: -0.4583333333 + 0.4583333333 + -0.5833333333x + x2 = 0 + 0.4583333333 Combine like terms: -0.4583333333 + 0.4583333333 = 0.0000000000 0.0000000000 + -0.5833333333x + x2 = 0 + 0.4583333333 -0.5833333333x + x2 = 0 + 0.4583333333 Combine like terms: 0 + 0.4583333333 = 0.4583333333 -0.5833333333x + x2 = 0.4583333333 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = 0.4583333333 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 0.4583333333 + 0.08506944446 Combine like terms: 0.4583333333 + 0.08506944446 = 0.54340277776 0.08506944446 + -0.5833333333x + x2 = 0.54340277776 Factor a perfect square on the left side: (x + -0.2916666667)(x + -0.2916666667) = 0.54340277776 Calculate the square root of the right side: 0.737158584 Break this problem into two subproblems by setting (x + -0.2916666667) equal to 0.737158584 and -0.737158584.Subproblem 1
x + -0.2916666667 = 0.737158584 Simplifying x + -0.2916666667 = 0.737158584 Reorder the terms: -0.2916666667 + x = 0.737158584 Solving -0.2916666667 + x = 0.737158584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 0.737158584 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 0.737158584 + 0.2916666667 x = 0.737158584 + 0.2916666667 Combine like terms: 0.737158584 + 0.2916666667 = 1.0288252507 x = 1.0288252507 Simplifying x = 1.0288252507Subproblem 2
x + -0.2916666667 = -0.737158584 Simplifying x + -0.2916666667 = -0.737158584 Reorder the terms: -0.2916666667 + x = -0.737158584 Solving -0.2916666667 + x = -0.737158584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -0.737158584 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -0.737158584 + 0.2916666667 x = -0.737158584 + 0.2916666667 Combine like terms: -0.737158584 + 0.2916666667 = -0.4454919173 x = -0.4454919173 Simplifying x = -0.4454919173Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0288252507, -0.4454919173}Solution
x = {1.0288252507, -0.4454919173}
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