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Simplifying -4.9x2 + 6.84x + 22 = 0 Reorder the terms: 22 + 6.84x + -4.9x2 = 0 Solving 22 + 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'. -4.489795918 + -1.395918367x + x2 = 0 Move the constant term to the right: Add '4.489795918' to each side of the equation. -4.489795918 + -1.395918367x + 4.489795918 + x2 = 0 + 4.489795918 Reorder the terms: -4.489795918 + 4.489795918 + -1.395918367x + x2 = 0 + 4.489795918 Combine like terms: -4.489795918 + 4.489795918 = 0.000000000 0.000000000 + -1.395918367x + x2 = 0 + 4.489795918 -1.395918367x + x2 = 0 + 4.489795918 Combine like terms: 0 + 4.489795918 = 4.489795918 -1.395918367x + x2 = 4.489795918 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 = 4.489795918 + 0.4871470218 Reorder the terms: 0.4871470218 + -1.395918367x + x2 = 4.489795918 + 0.4871470218 Combine like terms: 4.489795918 + 0.4871470218 = 4.9769429398 0.4871470218 + -1.395918367x + x2 = 4.9769429398 Factor a perfect square on the left side: (x + -0.6979591835)(x + -0.6979591835) = 4.9769429398 Calculate the square root of the right side: 2.230906305 Break this problem into two subproblems by setting (x + -0.6979591835) equal to 2.230906305 and -2.230906305.Subproblem 1
x + -0.6979591835 = 2.230906305 Simplifying x + -0.6979591835 = 2.230906305 Reorder the terms: -0.6979591835 + x = 2.230906305 Solving -0.6979591835 + x = 2.230906305 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 = 2.230906305 + 0.6979591835 Combine like terms: -0.6979591835 + 0.6979591835 = 0.0000000000 0.0000000000 + x = 2.230906305 + 0.6979591835 x = 2.230906305 + 0.6979591835 Combine like terms: 2.230906305 + 0.6979591835 = 2.9288654885 x = 2.9288654885 Simplifying x = 2.9288654885Subproblem 2
x + -0.6979591835 = -2.230906305 Simplifying x + -0.6979591835 = -2.230906305 Reorder the terms: -0.6979591835 + x = -2.230906305 Solving -0.6979591835 + x = -2.230906305 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 = -2.230906305 + 0.6979591835 Combine like terms: -0.6979591835 + 0.6979591835 = 0.0000000000 0.0000000000 + x = -2.230906305 + 0.6979591835 x = -2.230906305 + 0.6979591835 Combine like terms: -2.230906305 + 0.6979591835 = -1.5329471215 x = -1.5329471215 Simplifying x = -1.5329471215Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9288654885, -1.5329471215}
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