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Simplifying 4.9x2 + -18x + 6 = 0 Reorder the terms: 6 + -18x + 4.9x2 = 0 Solving 6 + -18x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 1.224489796 + -3.673469388x + x2 = 0 Move the constant term to the right: Add '-1.224489796' to each side of the equation. 1.224489796 + -3.673469388x + -1.224489796 + x2 = 0 + -1.224489796 Reorder the terms: 1.224489796 + -1.224489796 + -3.673469388x + x2 = 0 + -1.224489796 Combine like terms: 1.224489796 + -1.224489796 = 0.000000000 0.000000000 + -3.673469388x + x2 = 0 + -1.224489796 -3.673469388x + x2 = 0 + -1.224489796 Combine like terms: 0 + -1.224489796 = -1.224489796 -3.673469388x + x2 = -1.224489796 The x term is -3.673469388x. Take half its coefficient (-1.836734694). Square it (3.373594336) and add it to both sides. Add '3.373594336' to each side of the equation. -3.673469388x + 3.373594336 + x2 = -1.224489796 + 3.373594336 Reorder the terms: 3.373594336 + -3.673469388x + x2 = -1.224489796 + 3.373594336 Combine like terms: -1.224489796 + 3.373594336 = 2.14910454 3.373594336 + -3.673469388x + x2 = 2.14910454 Factor a perfect square on the left side: (x + -1.836734694)(x + -1.836734694) = 2.14910454 Calculate the square root of the right side: 1.465982449 Break this problem into two subproblems by setting (x + -1.836734694) equal to 1.465982449 and -1.465982449.Subproblem 1
x + -1.836734694 = 1.465982449 Simplifying x + -1.836734694 = 1.465982449 Reorder the terms: -1.836734694 + x = 1.465982449 Solving -1.836734694 + x = 1.465982449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + x = 1.465982449 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + x = 1.465982449 + 1.836734694 x = 1.465982449 + 1.836734694 Combine like terms: 1.465982449 + 1.836734694 = 3.302717143 x = 3.302717143 Simplifying x = 3.302717143Subproblem 2
x + -1.836734694 = -1.465982449 Simplifying x + -1.836734694 = -1.465982449 Reorder the terms: -1.836734694 + x = -1.465982449 Solving -1.836734694 + x = -1.465982449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + x = -1.465982449 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + x = -1.465982449 + 1.836734694 x = -1.465982449 + 1.836734694 Combine like terms: -1.465982449 + 1.836734694 = 0.370752245 x = 0.370752245 Simplifying x = 0.370752245Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.302717143, 0.370752245}
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