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Simplifying 44x2 + 5x + -10 = 0 Reorder the terms: -10 + 5x + 44x2 = 0 Solving -10 + 5x + 44x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. -0.2272727273 + 0.1136363636x + x2 = 0 Move the constant term to the right: Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.1136363636x + 0.2272727273 + x2 = 0 + 0.2272727273 Reorder the terms: -0.2272727273 + 0.2272727273 + 0.1136363636x + x2 = 0 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + 0.1136363636x + x2 = 0 + 0.2272727273 0.1136363636x + x2 = 0 + 0.2272727273 Combine like terms: 0 + 0.2272727273 = 0.2272727273 0.1136363636x + x2 = 0.2272727273 The x term is 0.1136363636x. Take half its coefficient (0.0568181818). Square it (0.003228305783) and add it to both sides. Add '0.003228305783' to each side of the equation. 0.1136363636x + 0.003228305783 + x2 = 0.2272727273 + 0.003228305783 Reorder the terms: 0.003228305783 + 0.1136363636x + x2 = 0.2272727273 + 0.003228305783 Combine like terms: 0.2272727273 + 0.003228305783 = 0.230501033083 0.003228305783 + 0.1136363636x + x2 = 0.230501033083 Factor a perfect square on the left side: (x + 0.0568181818)(x + 0.0568181818) = 0.230501033083 Calculate the square root of the right side: 0.480105231 Break this problem into two subproblems by setting (x + 0.0568181818) equal to 0.480105231 and -0.480105231.Subproblem 1
x + 0.0568181818 = 0.480105231 Simplifying x + 0.0568181818 = 0.480105231 Reorder the terms: 0.0568181818 + x = 0.480105231 Solving 0.0568181818 + x = 0.480105231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0568181818' to each side of the equation. 0.0568181818 + -0.0568181818 + x = 0.480105231 + -0.0568181818 Combine like terms: 0.0568181818 + -0.0568181818 = 0.0000000000 0.0000000000 + x = 0.480105231 + -0.0568181818 x = 0.480105231 + -0.0568181818 Combine like terms: 0.480105231 + -0.0568181818 = 0.4232870492 x = 0.4232870492 Simplifying x = 0.4232870492Subproblem 2
x + 0.0568181818 = -0.480105231 Simplifying x + 0.0568181818 = -0.480105231 Reorder the terms: 0.0568181818 + x = -0.480105231 Solving 0.0568181818 + x = -0.480105231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0568181818' to each side of the equation. 0.0568181818 + -0.0568181818 + x = -0.480105231 + -0.0568181818 Combine like terms: 0.0568181818 + -0.0568181818 = 0.0000000000 0.0000000000 + x = -0.480105231 + -0.0568181818 x = -0.480105231 + -0.0568181818 Combine like terms: -0.480105231 + -0.0568181818 = -0.5369234128 x = -0.5369234128 Simplifying x = -0.5369234128Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4232870492, -0.5369234128}
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