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Simplifying 1.245x2 + -58.27x + 322.0352 = 0 Reorder the terms: 322.0352 + -58.27x + 1.245x2 = 0 Solving 322.0352 + -58.27x + 1.245x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.245 the coefficient of the squared term: Divide each side by '1.245'. 258.6628112 + -46.80321285x + x2 = 0 Move the constant term to the right: Add '-258.6628112' to each side of the equation. 258.6628112 + -46.80321285x + -258.6628112 + x2 = 0 + -258.6628112 Reorder the terms: 258.6628112 + -258.6628112 + -46.80321285x + x2 = 0 + -258.6628112 Combine like terms: 258.6628112 + -258.6628112 = 0.0000000 0.0000000 + -46.80321285x + x2 = 0 + -258.6628112 -46.80321285x + x2 = 0 + -258.6628112 Combine like terms: 0 + -258.6628112 = -258.6628112 -46.80321285x + x2 = -258.6628112 The x term is -46.80321285x. Take half its coefficient (-23.40160643). Square it (547.6351835) and add it to both sides. Add '547.6351835' to each side of the equation. -46.80321285x + 547.6351835 + x2 = -258.6628112 + 547.6351835 Reorder the terms: 547.6351835 + -46.80321285x + x2 = -258.6628112 + 547.6351835 Combine like terms: -258.6628112 + 547.6351835 = 288.9723723 547.6351835 + -46.80321285x + x2 = 288.9723723 Factor a perfect square on the left side: (x + -23.40160643)(x + -23.40160643) = 288.9723723 Calculate the square root of the right side: 16.999187401 Break this problem into two subproblems by setting (x + -23.40160643) equal to 16.999187401 and -16.999187401.Subproblem 1
x + -23.40160643 = 16.999187401 Simplifying x + -23.40160643 = 16.999187401 Reorder the terms: -23.40160643 + x = 16.999187401 Solving -23.40160643 + x = 16.999187401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.40160643' to each side of the equation. -23.40160643 + 23.40160643 + x = 16.999187401 + 23.40160643 Combine like terms: -23.40160643 + 23.40160643 = 0.00000000 0.00000000 + x = 16.999187401 + 23.40160643 x = 16.999187401 + 23.40160643 Combine like terms: 16.999187401 + 23.40160643 = 40.400793831 x = 40.400793831 Simplifying x = 40.400793831Subproblem 2
x + -23.40160643 = -16.999187401 Simplifying x + -23.40160643 = -16.999187401 Reorder the terms: -23.40160643 + x = -16.999187401 Solving -23.40160643 + x = -16.999187401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23.40160643' to each side of the equation. -23.40160643 + 23.40160643 + x = -16.999187401 + 23.40160643 Combine like terms: -23.40160643 + 23.40160643 = 0.00000000 0.00000000 + x = -16.999187401 + 23.40160643 x = -16.999187401 + 23.40160643 Combine like terms: -16.999187401 + 23.40160643 = 6.402419029 x = 6.402419029 Simplifying x = 6.402419029Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.400793831, 6.402419029}
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