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Simplifying 2x2 + 40.32x = 221 Reorder the terms: 40.32x + 2x2 = 221 Solving 40.32x + 2x2 = 221 Solving for variable 'x'. Reorder the terms: -221 + 40.32x + 2x2 = 221 + -221 Combine like terms: 221 + -221 = 0 -221 + 40.32x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -110.5 + 20.16x + x2 = 0 Move the constant term to the right: Add '110.5' to each side of the equation. -110.5 + 20.16x + 110.5 + x2 = 0 + 110.5 Reorder the terms: -110.5 + 110.5 + 20.16x + x2 = 0 + 110.5 Combine like terms: -110.5 + 110.5 = 0.0 0.0 + 20.16x + x2 = 0 + 110.5 20.16x + x2 = 0 + 110.5 Combine like terms: 0 + 110.5 = 110.5 20.16x + x2 = 110.5 The x term is 20.16x. Take half its coefficient (10.08). Square it (101.6064) and add it to both sides. Add '101.6064' to each side of the equation. 20.16x + 101.6064 + x2 = 110.5 + 101.6064 Reorder the terms: 101.6064 + 20.16x + x2 = 110.5 + 101.6064 Combine like terms: 110.5 + 101.6064 = 212.1064 101.6064 + 20.16x + x2 = 212.1064 Factor a perfect square on the left side: (x + 10.08)(x + 10.08) = 212.1064 Calculate the square root of the right side: 14.563873111 Break this problem into two subproblems by setting (x + 10.08) equal to 14.563873111 and -14.563873111.Subproblem 1
x + 10.08 = 14.563873111 Simplifying x + 10.08 = 14.563873111 Reorder the terms: 10.08 + x = 14.563873111 Solving 10.08 + x = 14.563873111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.08' to each side of the equation. 10.08 + -10.08 + x = 14.563873111 + -10.08 Combine like terms: 10.08 + -10.08 = 0.00 0.00 + x = 14.563873111 + -10.08 x = 14.563873111 + -10.08 Combine like terms: 14.563873111 + -10.08 = 4.483873111 x = 4.483873111 Simplifying x = 4.483873111Subproblem 2
x + 10.08 = -14.563873111 Simplifying x + 10.08 = -14.563873111 Reorder the terms: 10.08 + x = -14.563873111 Solving 10.08 + x = -14.563873111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.08' to each side of the equation. 10.08 + -10.08 + x = -14.563873111 + -10.08 Combine like terms: 10.08 + -10.08 = 0.00 0.00 + x = -14.563873111 + -10.08 x = -14.563873111 + -10.08 Combine like terms: -14.563873111 + -10.08 = -24.643873111 x = -24.643873111 Simplifying x = -24.643873111Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.483873111, -24.643873111}
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