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Simplifying 3.9 = 18x + -4.9x2 Solving 3.9 = 18x + -4.9x2 Solving for variable 'x'. Reorder the terms: 3.9 + -18x + 4.9x2 = 18x + -18x + -4.9x2 + 4.9x2 Combine like terms: 18x + -18x = 0 3.9 + -18x + 4.9x2 = 0 + -4.9x2 + 4.9x2 3.9 + -18x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 3.9 + -18x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 0.7959183673 + -3.673469388x + x2 = 0 Move the constant term to the right: Add '-0.7959183673' to each side of the equation. 0.7959183673 + -3.673469388x + -0.7959183673 + x2 = 0 + -0.7959183673 Reorder the terms: 0.7959183673 + -0.7959183673 + -3.673469388x + x2 = 0 + -0.7959183673 Combine like terms: 0.7959183673 + -0.7959183673 = 0.0000000000 0.0000000000 + -3.673469388x + x2 = 0 + -0.7959183673 -3.673469388x + x2 = 0 + -0.7959183673 Combine like terms: 0 + -0.7959183673 = -0.7959183673 -3.673469388x + x2 = -0.7959183673 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 = -0.7959183673 + 3.373594336 Reorder the terms: 3.373594336 + -3.673469388x + x2 = -0.7959183673 + 3.373594336 Combine like terms: -0.7959183673 + 3.373594336 = 2.5776759687 3.373594336 + -3.673469388x + x2 = 2.5776759687 Factor a perfect square on the left side: (x + -1.836734694)(x + -1.836734694) = 2.5776759687 Calculate the square root of the right side: 1.605514238 Break this problem into two subproblems by setting (x + -1.836734694) equal to 1.605514238 and -1.605514238.Subproblem 1
x + -1.836734694 = 1.605514238 Simplifying x + -1.836734694 = 1.605514238 Reorder the terms: -1.836734694 + x = 1.605514238 Solving -1.836734694 + x = 1.605514238 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 = 1.605514238 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + x = 1.605514238 + 1.836734694 x = 1.605514238 + 1.836734694 Combine like terms: 1.605514238 + 1.836734694 = 3.442248932 x = 3.442248932 Simplifying x = 3.442248932Subproblem 2
x + -1.836734694 = -1.605514238 Simplifying x + -1.836734694 = -1.605514238 Reorder the terms: -1.836734694 + x = -1.605514238 Solving -1.836734694 + x = -1.605514238 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 = -1.605514238 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + x = -1.605514238 + 1.836734694 x = -1.605514238 + 1.836734694 Combine like terms: -1.605514238 + 1.836734694 = 0.231220456 x = 0.231220456 Simplifying x = 0.231220456Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.442248932, 0.231220456}
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