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Simplifying 1.9x2 + 6x + -6 = 0 Reorder the terms: -6 + 6x + 1.9x2 = 0 Solving -6 + 6x + 1.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.9 the coefficient of the squared term: Divide each side by '1.9'. -3.157894737 + 3.157894737x + x2 = 0 Move the constant term to the right: Add '3.157894737' to each side of the equation. -3.157894737 + 3.157894737x + 3.157894737 + x2 = 0 + 3.157894737 Reorder the terms: -3.157894737 + 3.157894737 + 3.157894737x + x2 = 0 + 3.157894737 Combine like terms: -3.157894737 + 3.157894737 = 0.000000000 0.000000000 + 3.157894737x + x2 = 0 + 3.157894737 3.157894737x + x2 = 0 + 3.157894737 Combine like terms: 0 + 3.157894737 = 3.157894737 3.157894737x + x2 = 3.157894737 The x term is 3.157894737x. Take half its coefficient (1.578947369). Square it (2.493074794) and add it to both sides. Add '2.493074794' to each side of the equation. 3.157894737x + 2.493074794 + x2 = 3.157894737 + 2.493074794 Reorder the terms: 2.493074794 + 3.157894737x + x2 = 3.157894737 + 2.493074794 Combine like terms: 3.157894737 + 2.493074794 = 5.650969531 2.493074794 + 3.157894737x + x2 = 5.650969531 Factor a perfect square on the left side: (x + 1.578947369)(x + 1.578947369) = 5.650969531 Calculate the square root of the right side: 2.377176798 Break this problem into two subproblems by setting (x + 1.578947369) equal to 2.377176798 and -2.377176798.Subproblem 1
x + 1.578947369 = 2.377176798 Simplifying x + 1.578947369 = 2.377176798 Reorder the terms: 1.578947369 + x = 2.377176798 Solving 1.578947369 + x = 2.377176798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.578947369' to each side of the equation. 1.578947369 + -1.578947369 + x = 2.377176798 + -1.578947369 Combine like terms: 1.578947369 + -1.578947369 = 0.000000000 0.000000000 + x = 2.377176798 + -1.578947369 x = 2.377176798 + -1.578947369 Combine like terms: 2.377176798 + -1.578947369 = 0.798229429 x = 0.798229429 Simplifying x = 0.798229429Subproblem 2
x + 1.578947369 = -2.377176798 Simplifying x + 1.578947369 = -2.377176798 Reorder the terms: 1.578947369 + x = -2.377176798 Solving 1.578947369 + x = -2.377176798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.578947369' to each side of the equation. 1.578947369 + -1.578947369 + x = -2.377176798 + -1.578947369 Combine like terms: 1.578947369 + -1.578947369 = 0.000000000 0.000000000 + x = -2.377176798 + -1.578947369 x = -2.377176798 + -1.578947369 Combine like terms: -2.377176798 + -1.578947369 = -3.956124167 x = -3.956124167 Simplifying x = -3.956124167Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.798229429, -3.956124167}
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