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Simplifying 30 + 6.84x + -4.9x2 = 0 Solving 30 + 6.84x + -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'. -6.12244898 + -1.395918367x + x2 = 0 Move the constant term to the right: Add '6.12244898' to each side of the equation. -6.12244898 + -1.395918367x + 6.12244898 + x2 = 0 + 6.12244898 Reorder the terms: -6.12244898 + 6.12244898 + -1.395918367x + x2 = 0 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + -1.395918367x + x2 = 0 + 6.12244898 -1.395918367x + x2 = 0 + 6.12244898 Combine like terms: 0 + 6.12244898 = 6.12244898 -1.395918367x + x2 = 6.12244898 The x term is -1.395918367x. Take half its coefficient (-0.6979591835). Square it (0.4871470218) and add it to both sides. Add '0.4871470218' to each side of the equation. -1.395918367x + 0.4871470218 + x2 = 6.12244898 + 0.4871470218 Reorder the terms: 0.4871470218 + -1.395918367x + x2 = 6.12244898 + 0.4871470218 Combine like terms: 6.12244898 + 0.4871470218 = 6.6095960018 0.4871470218 + -1.395918367x + x2 = 6.6095960018 Factor a perfect square on the left side: (x + -0.6979591835)(x + -0.6979591835) = 6.6095960018 Calculate the square root of the right side: 2.570913457 Break this problem into two subproblems by setting (x + -0.6979591835) equal to 2.570913457 and -2.570913457.Subproblem 1
x + -0.6979591835 = 2.570913457 Simplifying x + -0.6979591835 = 2.570913457 Reorder the terms: -0.6979591835 + x = 2.570913457 Solving -0.6979591835 + x = 2.570913457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6979591835' to each side of the equation. -0.6979591835 + 0.6979591835 + x = 2.570913457 + 0.6979591835 Combine like terms: -0.6979591835 + 0.6979591835 = 0.0000000000 0.0000000000 + x = 2.570913457 + 0.6979591835 x = 2.570913457 + 0.6979591835 Combine like terms: 2.570913457 + 0.6979591835 = 3.2688726405 x = 3.2688726405 Simplifying x = 3.2688726405Subproblem 2
x + -0.6979591835 = -2.570913457 Simplifying x + -0.6979591835 = -2.570913457 Reorder the terms: -0.6979591835 + x = -2.570913457 Solving -0.6979591835 + x = -2.570913457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6979591835' to each side of the equation. -0.6979591835 + 0.6979591835 + x = -2.570913457 + 0.6979591835 Combine like terms: -0.6979591835 + 0.6979591835 = 0.0000000000 0.0000000000 + x = -2.570913457 + 0.6979591835 x = -2.570913457 + 0.6979591835 Combine like terms: -2.570913457 + 0.6979591835 = -1.8729542735 x = -1.8729542735 Simplifying x = -1.8729542735Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2688726405, -1.8729542735}
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