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Simplifying 22.23 = 2x2 + x Reorder the terms: 22.23 = x + 2x2 Solving 22.23 = x + 2x2 Solving for variable 'x'. Reorder the terms: 22.23 + -1x + -2x2 = x + -1x + 2x2 + -2x2 Combine like terms: x + -1x = 0 22.23 + -1x + -2x2 = 0 + 2x2 + -2x2 22.23 + -1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 22.23 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -11.115 + 0.5x + x2 = 0 Move the constant term to the right: Add '11.115' to each side of the equation. -11.115 + 0.5x + 11.115 + x2 = 0 + 11.115 Reorder the terms: -11.115 + 11.115 + 0.5x + x2 = 0 + 11.115 Combine like terms: -11.115 + 11.115 = 0.000 0.000 + 0.5x + x2 = 0 + 11.115 0.5x + x2 = 0 + 11.115 Combine like terms: 0 + 11.115 = 11.115 0.5x + x2 = 11.115 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 11.115 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 11.115 + 0.0625 Combine like terms: 11.115 + 0.0625 = 11.1775 0.0625 + 0.5x + x2 = 11.1775 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 11.1775 Calculate the square root of the right side: 3.343276836 Break this problem into two subproblems by setting (x + 0.25) equal to 3.343276836 and -3.343276836.Subproblem 1
x + 0.25 = 3.343276836 Simplifying x + 0.25 = 3.343276836 Reorder the terms: 0.25 + x = 3.343276836 Solving 0.25 + x = 3.343276836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 3.343276836 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.343276836 + -0.25 x = 3.343276836 + -0.25 Combine like terms: 3.343276836 + -0.25 = 3.093276836 x = 3.093276836 Simplifying x = 3.093276836Subproblem 2
x + 0.25 = -3.343276836 Simplifying x + 0.25 = -3.343276836 Reorder the terms: 0.25 + x = -3.343276836 Solving 0.25 + x = -3.343276836 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -3.343276836 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.343276836 + -0.25 x = -3.343276836 + -0.25 Combine like terms: -3.343276836 + -0.25 = -3.593276836 x = -3.593276836 Simplifying x = -3.593276836Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.093276836, -3.593276836}
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