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Simplifying -4.9x2 + 5x + 9 = 0 Reorder the terms: 9 + 5x + -4.9x2 = 0 Solving 9 + 5x + -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'. -1.836734694 + -1.020408163x + x2 = 0 Move the constant term to the right: Add '1.836734694' to each side of the equation. -1.836734694 + -1.020408163x + 1.836734694 + x2 = 0 + 1.836734694 Reorder the terms: -1.836734694 + 1.836734694 + -1.020408163x + x2 = 0 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + -1.020408163x + x2 = 0 + 1.836734694 -1.020408163x + x2 = 0 + 1.836734694 Combine like terms: 0 + 1.836734694 = 1.836734694 -1.020408163x + x2 = 1.836734694 The x term is -1.020408163x. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163x + 0.2603082048 + x2 = 1.836734694 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163x + x2 = 1.836734694 + 0.2603082048 Combine like terms: 1.836734694 + 0.2603082048 = 2.0970428988 0.2603082048 + -1.020408163x + x2 = 2.0970428988 Factor a perfect square on the left side: (x + -0.5102040815)(x + -0.5102040815) = 2.0970428988 Calculate the square root of the right side: 1.448117018 Break this problem into two subproblems by setting (x + -0.5102040815) equal to 1.448117018 and -1.448117018.Subproblem 1
x + -0.5102040815 = 1.448117018 Simplifying x + -0.5102040815 = 1.448117018 Reorder the terms: -0.5102040815 + x = 1.448117018 Solving -0.5102040815 + x = 1.448117018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = 1.448117018 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = 1.448117018 + 0.5102040815 x = 1.448117018 + 0.5102040815 Combine like terms: 1.448117018 + 0.5102040815 = 1.9583210995 x = 1.9583210995 Simplifying x = 1.9583210995Subproblem 2
x + -0.5102040815 = -1.448117018 Simplifying x + -0.5102040815 = -1.448117018 Reorder the terms: -0.5102040815 + x = -1.448117018 Solving -0.5102040815 + x = -1.448117018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + x = -1.448117018 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = -1.448117018 + 0.5102040815 x = -1.448117018 + 0.5102040815 Combine like terms: -1.448117018 + 0.5102040815 = -0.9379129365 x = -0.9379129365 Simplifying x = -0.9379129365Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9583210995, -0.9379129365}
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