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Simplifying 4.9x2 + 18x + -8.26 = 0 Reorder the terms: -8.26 + 18x + 4.9x2 = 0 Solving -8.26 + 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'. -1.685714286 + 3.673469388x + x2 = 0 Move the constant term to the right: Add '1.685714286' to each side of the equation. -1.685714286 + 3.673469388x + 1.685714286 + x2 = 0 + 1.685714286 Reorder the terms: -1.685714286 + 1.685714286 + 3.673469388x + x2 = 0 + 1.685714286 Combine like terms: -1.685714286 + 1.685714286 = 0.000000000 0.000000000 + 3.673469388x + x2 = 0 + 1.685714286 3.673469388x + x2 = 0 + 1.685714286 Combine like terms: 0 + 1.685714286 = 1.685714286 3.673469388x + x2 = 1.685714286 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 = 1.685714286 + 3.373594336 Reorder the terms: 3.373594336 + 3.673469388x + x2 = 1.685714286 + 3.373594336 Combine like terms: 1.685714286 + 3.373594336 = 5.059308622 3.373594336 + 3.673469388x + x2 = 5.059308622 Factor a perfect square on the left side: (x + 1.836734694)(x + 1.836734694) = 5.059308622 Calculate the square root of the right side: 2.249290693 Break this problem into two subproblems by setting (x + 1.836734694) equal to 2.249290693 and -2.249290693.Subproblem 1
x + 1.836734694 = 2.249290693 Simplifying x + 1.836734694 = 2.249290693 Reorder the terms: 1.836734694 + x = 2.249290693 Solving 1.836734694 + x = 2.249290693 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 = 2.249290693 + -1.836734694 Combine like terms: 1.836734694 + -1.836734694 = 0.000000000 0.000000000 + x = 2.249290693 + -1.836734694 x = 2.249290693 + -1.836734694 Combine like terms: 2.249290693 + -1.836734694 = 0.412555999 x = 0.412555999 Simplifying x = 0.412555999Subproblem 2
x + 1.836734694 = -2.249290693 Simplifying x + 1.836734694 = -2.249290693 Reorder the terms: 1.836734694 + x = -2.249290693 Solving 1.836734694 + x = -2.249290693 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 = -2.249290693 + -1.836734694 Combine like terms: 1.836734694 + -1.836734694 = 0.000000000 0.000000000 + x = -2.249290693 + -1.836734694 x = -2.249290693 + -1.836734694 Combine like terms: -2.249290693 + -1.836734694 = -4.086025387 x = -4.086025387 Simplifying x = -4.086025387Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.412555999, -4.086025387}
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