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Simplifying 49x2 + -14x + 1 + -1(7x + 1)(3x + -50) = 0 Reorder the terms: 49x2 + -14x + 1 + -1(1 + 7x)(3x + -50) = 0 Reorder the terms: 49x2 + -14x + 1 + -1(1 + 7x)(-50 + 3x) = 0 Multiply (1 + 7x) * (-50 + 3x) 49x2 + -14x + 1 + -1(1(-50 + 3x) + 7x * (-50 + 3x)) = 0 49x2 + -14x + 1 + -1((-50 * 1 + 3x * 1) + 7x * (-50 + 3x)) = 0 49x2 + -14x + 1 + -1((-50 + 3x) + 7x * (-50 + 3x)) = 0 49x2 + -14x + 1 + -1(-50 + 3x + (-50 * 7x + 3x * 7x)) = 0 49x2 + -14x + 1 + -1(-50 + 3x + (-350x + 21x2)) = 0 Combine like terms: 3x + -350x = -347x 49x2 + -14x + 1 + -1(-50 + -347x + 21x2) = 0 49x2 + -14x + 1 + (-50 * -1 + -347x * -1 + 21x2 * -1) = 0 49x2 + -14x + 1 + (50 + 347x + -21x2) = 0 Reorder the terms: 1 + 50 + -14x + 347x + 49x2 + -21x2 = 0 Combine like terms: 1 + 50 = 51 51 + -14x + 347x + 49x2 + -21x2 = 0 Combine like terms: -14x + 347x = 333x 51 + 333x + 49x2 + -21x2 = 0 Combine like terms: 49x2 + -21x2 = 28x2 51 + 333x + 28x2 = 0 Solving 51 + 333x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 1.821428571 + 11.89285714x + x2 = 0 Move the constant term to the right: Add '-1.821428571' to each side of the equation. 1.821428571 + 11.89285714x + -1.821428571 + x2 = 0 + -1.821428571 Reorder the terms: 1.821428571 + -1.821428571 + 11.89285714x + x2 = 0 + -1.821428571 Combine like terms: 1.821428571 + -1.821428571 = 0.000000000 0.000000000 + 11.89285714x + x2 = 0 + -1.821428571 11.89285714x + x2 = 0 + -1.821428571 Combine like terms: 0 + -1.821428571 = -1.821428571 11.89285714x + x2 = -1.821428571 The x term is 11.89285714x. Take half its coefficient (5.94642857). Square it (35.36001274) and add it to both sides. Add '35.36001274' to each side of the equation. 11.89285714x + 35.36001274 + x2 = -1.821428571 + 35.36001274 Reorder the terms: 35.36001274 + 11.89285714x + x2 = -1.821428571 + 35.36001274 Combine like terms: -1.821428571 + 35.36001274 = 33.538584169 35.36001274 + 11.89285714x + x2 = 33.538584169 Factor a perfect square on the left side: (x + 5.94642857)(x + 5.94642857) = 33.538584169 Calculate the square root of the right side: 5.791250657 Break this problem into two subproblems by setting (x + 5.94642857) equal to 5.791250657 and -5.791250657.Subproblem 1
x + 5.94642857 = 5.791250657 Simplifying x + 5.94642857 = 5.791250657 Reorder the terms: 5.94642857 + x = 5.791250657 Solving 5.94642857 + x = 5.791250657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.94642857' to each side of the equation. 5.94642857 + -5.94642857 + x = 5.791250657 + -5.94642857 Combine like terms: 5.94642857 + -5.94642857 = 0.00000000 0.00000000 + x = 5.791250657 + -5.94642857 x = 5.791250657 + -5.94642857 Combine like terms: 5.791250657 + -5.94642857 = -0.155177913 x = -0.155177913 Simplifying x = -0.155177913Subproblem 2
x + 5.94642857 = -5.791250657 Simplifying x + 5.94642857 = -5.791250657 Reorder the terms: 5.94642857 + x = -5.791250657 Solving 5.94642857 + x = -5.791250657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.94642857' to each side of the equation. 5.94642857 + -5.94642857 + x = -5.791250657 + -5.94642857 Combine like terms: 5.94642857 + -5.94642857 = 0.00000000 0.00000000 + x = -5.791250657 + -5.94642857 x = -5.791250657 + -5.94642857 Combine like terms: -5.791250657 + -5.94642857 = -11.737679227 x = -11.737679227 Simplifying x = -11.737679227Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.155177913, -11.737679227}
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