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Simplifying -490x2 + 75x + 12 = 0 Reorder the terms: 12 + 75x + -490x2 = 0 Solving 12 + 75x + -490x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -490 the coefficient of the squared term: Divide each side by '-490'. -0.02448979592 + -0.1530612245x + x2 = 0 Move the constant term to the right: Add '0.02448979592' to each side of the equation. -0.02448979592 + -0.1530612245x + 0.02448979592 + x2 = 0 + 0.02448979592 Reorder the terms: -0.02448979592 + 0.02448979592 + -0.1530612245x + x2 = 0 + 0.02448979592 Combine like terms: -0.02448979592 + 0.02448979592 = 0.00000000000 0.00000000000 + -0.1530612245x + x2 = 0 + 0.02448979592 -0.1530612245x + x2 = 0 + 0.02448979592 Combine like terms: 0 + 0.02448979592 = 0.02448979592 -0.1530612245x + x2 = 0.02448979592 The x term is -0.1530612245x. Take half its coefficient (-0.07653061225). Square it (0.005856934611) and add it to both sides. Add '0.005856934611' to each side of the equation. -0.1530612245x + 0.005856934611 + x2 = 0.02448979592 + 0.005856934611 Reorder the terms: 0.005856934611 + -0.1530612245x + x2 = 0.02448979592 + 0.005856934611 Combine like terms: 0.02448979592 + 0.005856934611 = 0.030346730531 0.005856934611 + -0.1530612245x + x2 = 0.030346730531 Factor a perfect square on the left side: (x + -0.07653061225)(x + -0.07653061225) = 0.030346730531 Calculate the square root of the right side: 0.17420313 Break this problem into two subproblems by setting (x + -0.07653061225) equal to 0.17420313 and -0.17420313.Subproblem 1
x + -0.07653061225 = 0.17420313 Simplifying x + -0.07653061225 = 0.17420313 Reorder the terms: -0.07653061225 + x = 0.17420313 Solving -0.07653061225 + x = 0.17420313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07653061225' to each side of the equation. -0.07653061225 + 0.07653061225 + x = 0.17420313 + 0.07653061225 Combine like terms: -0.07653061225 + 0.07653061225 = 0.00000000000 0.00000000000 + x = 0.17420313 + 0.07653061225 x = 0.17420313 + 0.07653061225 Combine like terms: 0.17420313 + 0.07653061225 = 0.25073374225 x = 0.25073374225 Simplifying x = 0.25073374225Subproblem 2
x + -0.07653061225 = -0.17420313 Simplifying x + -0.07653061225 = -0.17420313 Reorder the terms: -0.07653061225 + x = -0.17420313 Solving -0.07653061225 + x = -0.17420313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07653061225' to each side of the equation. -0.07653061225 + 0.07653061225 + x = -0.17420313 + 0.07653061225 Combine like terms: -0.07653061225 + 0.07653061225 = 0.00000000000 0.00000000000 + x = -0.17420313 + 0.07653061225 x = -0.17420313 + 0.07653061225 Combine like terms: -0.17420313 + 0.07653061225 = -0.09767251775 x = -0.09767251775 Simplifying x = -0.09767251775Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.25073374225, -0.09767251775}
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