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Simplifying 4.9x2 + -9x + -6 = 0 Reorder the terms: -6 + -9x + 4.9x2 = 0 Solving -6 + -9x + 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'. -1.224489796 + -1.836734694x + x2 = 0 Move the constant term to the right: Add '1.224489796' to each side of the equation. -1.224489796 + -1.836734694x + 1.224489796 + x2 = 0 + 1.224489796 Reorder the terms: -1.224489796 + 1.224489796 + -1.836734694x + x2 = 0 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + -1.836734694x + x2 = 0 + 1.224489796 -1.836734694x + x2 = 0 + 1.224489796 Combine like terms: 0 + 1.224489796 = 1.224489796 -1.836734694x + x2 = 1.224489796 The x term is -1.836734694x. Take half its coefficient (-0.918367347). Square it (0.8433985840) and add it to both sides. Add '0.8433985840' to each side of the equation. -1.836734694x + 0.8433985840 + x2 = 1.224489796 + 0.8433985840 Reorder the terms: 0.8433985840 + -1.836734694x + x2 = 1.224489796 + 0.8433985840 Combine like terms: 1.224489796 + 0.8433985840 = 2.06788838 0.8433985840 + -1.836734694x + x2 = 2.06788838 Factor a perfect square on the left side: (x + -0.918367347)(x + -0.918367347) = 2.06788838 Calculate the square root of the right side: 1.438015431 Break this problem into two subproblems by setting (x + -0.918367347) equal to 1.438015431 and -1.438015431.Subproblem 1
x + -0.918367347 = 1.438015431 Simplifying x + -0.918367347 = 1.438015431 Reorder the terms: -0.918367347 + x = 1.438015431 Solving -0.918367347 + x = 1.438015431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = 1.438015431 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = 1.438015431 + 0.918367347 x = 1.438015431 + 0.918367347 Combine like terms: 1.438015431 + 0.918367347 = 2.356382778 x = 2.356382778 Simplifying x = 2.356382778Subproblem 2
x + -0.918367347 = -1.438015431 Simplifying x + -0.918367347 = -1.438015431 Reorder the terms: -0.918367347 + x = -1.438015431 Solving -0.918367347 + x = -1.438015431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = -1.438015431 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = -1.438015431 + 0.918367347 x = -1.438015431 + 0.918367347 Combine like terms: -1.438015431 + 0.918367347 = -0.519648084 x = -0.519648084 Simplifying x = -0.519648084Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.356382778, -0.519648084}
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