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Simplifying -4.9x2 + 4.6x + 2.1 = 0 Reorder the terms: 2.1 + 4.6x + -4.9x2 = 0 Solving 2.1 + 4.6x + -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'. -0.4285714286 + -0.9387755102x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.9387755102x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.9387755102x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.9387755102x + x2 = 0 + 0.4285714286 -0.9387755102x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.9387755102x + x2 = 0.4285714286 The x term is -0.9387755102x. Take half its coefficient (-0.4693877551). Square it (0.2203248646) and add it to both sides. Add '0.2203248646' to each side of the equation. -0.9387755102x + 0.2203248646 + x2 = 0.4285714286 + 0.2203248646 Reorder the terms: 0.2203248646 + -0.9387755102x + x2 = 0.4285714286 + 0.2203248646 Combine like terms: 0.4285714286 + 0.2203248646 = 0.6488962932 0.2203248646 + -0.9387755102x + x2 = 0.6488962932 Factor a perfect square on the left side: (x + -0.4693877551)(x + -0.4693877551) = 0.6488962932 Calculate the square root of the right side: 0.805540994 Break this problem into two subproblems by setting (x + -0.4693877551) equal to 0.805540994 and -0.805540994.Subproblem 1
x + -0.4693877551 = 0.805540994 Simplifying x + -0.4693877551 = 0.805540994 Reorder the terms: -0.4693877551 + x = 0.805540994 Solving -0.4693877551 + x = 0.805540994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4693877551' to each side of the equation. -0.4693877551 + 0.4693877551 + x = 0.805540994 + 0.4693877551 Combine like terms: -0.4693877551 + 0.4693877551 = 0.0000000000 0.0000000000 + x = 0.805540994 + 0.4693877551 x = 0.805540994 + 0.4693877551 Combine like terms: 0.805540994 + 0.4693877551 = 1.2749287491 x = 1.2749287491 Simplifying x = 1.2749287491Subproblem 2
x + -0.4693877551 = -0.805540994 Simplifying x + -0.4693877551 = -0.805540994 Reorder the terms: -0.4693877551 + x = -0.805540994 Solving -0.4693877551 + x = -0.805540994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4693877551' to each side of the equation. -0.4693877551 + 0.4693877551 + x = -0.805540994 + 0.4693877551 Combine like terms: -0.4693877551 + 0.4693877551 = 0.0000000000 0.0000000000 + x = -0.805540994 + 0.4693877551 x = -0.805540994 + 0.4693877551 Combine like terms: -0.805540994 + 0.4693877551 = -0.3361532389 x = -0.3361532389 Simplifying x = -0.3361532389Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2749287491, -0.3361532389}
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