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Simplifying 0.66 = x2 + 3.33x Reorder the terms: 0.66 = 3.33x + x2 Solving 0.66 = 3.33x + x2 Solving for variable 'x'. Reorder the terms: 0.66 + -3.33x + -1x2 = 3.33x + -3.33x + x2 + -1x2 Combine like terms: 3.33x + -3.33x = 0.00 0.66 + -3.33x + -1x2 = 0.00 + x2 + -1x2 0.66 + -3.33x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.66 + -3.33x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.66 + 3.33x + x2 = 0 Move the constant term to the right: Add '0.66' to each side of the equation. -0.66 + 3.33x + 0.66 + x2 = 0 + 0.66 Reorder the terms: -0.66 + 0.66 + 3.33x + x2 = 0 + 0.66 Combine like terms: -0.66 + 0.66 = 0.00 0.00 + 3.33x + x2 = 0 + 0.66 3.33x + x2 = 0 + 0.66 Combine like terms: 0 + 0.66 = 0.66 3.33x + x2 = 0.66 The x term is 3.33x. Take half its coefficient (1.665). Square it (2.772225) and add it to both sides. Add '2.772225' to each side of the equation. 3.33x + 2.772225 + x2 = 0.66 + 2.772225 Reorder the terms: 2.772225 + 3.33x + x2 = 0.66 + 2.772225 Combine like terms: 0.66 + 2.772225 = 3.432225 2.772225 + 3.33x + x2 = 3.432225 Factor a perfect square on the left side: (x + 1.665)(x + 1.665) = 3.432225 Calculate the square root of the right side: 1.852626514 Break this problem into two subproblems by setting (x + 1.665) equal to 1.852626514 and -1.852626514.Subproblem 1
x + 1.665 = 1.852626514 Simplifying x + 1.665 = 1.852626514 Reorder the terms: 1.665 + x = 1.852626514 Solving 1.665 + x = 1.852626514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.665' to each side of the equation. 1.665 + -1.665 + x = 1.852626514 + -1.665 Combine like terms: 1.665 + -1.665 = 0.000 0.000 + x = 1.852626514 + -1.665 x = 1.852626514 + -1.665 Combine like terms: 1.852626514 + -1.665 = 0.187626514 x = 0.187626514 Simplifying x = 0.187626514Subproblem 2
x + 1.665 = -1.852626514 Simplifying x + 1.665 = -1.852626514 Reorder the terms: 1.665 + x = -1.852626514 Solving 1.665 + x = -1.852626514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.665' to each side of the equation. 1.665 + -1.665 + x = -1.852626514 + -1.665 Combine like terms: 1.665 + -1.665 = 0.000 0.000 + x = -1.852626514 + -1.665 x = -1.852626514 + -1.665 Combine like terms: -1.852626514 + -1.665 = -3.517626514 x = -3.517626514 Simplifying x = -3.517626514Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.187626514, -3.517626514}
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