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Simplifying 20x2 + -11x = 6 Reorder the terms: -11x + 20x2 = 6 Solving -11x + 20x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + -11x + 20x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -11x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.3 + -0.55x + x2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.55x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.55x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.55x + x2 = 0 + 0.3 -0.55x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 -0.55x + x2 = 0.3 The x term is -0.55x. Take half its coefficient (-0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. -0.55x + 0.075625 + x2 = 0.3 + 0.075625 Reorder the terms: 0.075625 + -0.55x + x2 = 0.3 + 0.075625 Combine like terms: 0.3 + 0.075625 = 0.375625 0.075625 + -0.55x + x2 = 0.375625 Factor a perfect square on the left side: (x + -0.275)(x + -0.275) = 0.375625 Calculate the square root of the right side: 0.612882534 Break this problem into two subproblems by setting (x + -0.275) equal to 0.612882534 and -0.612882534.Subproblem 1
x + -0.275 = 0.612882534 Simplifying x + -0.275 = 0.612882534 Reorder the terms: -0.275 + x = 0.612882534 Solving -0.275 + x = 0.612882534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x = 0.612882534 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x = 0.612882534 + 0.275 x = 0.612882534 + 0.275 Combine like terms: 0.612882534 + 0.275 = 0.887882534 x = 0.887882534 Simplifying x = 0.887882534Subproblem 2
x + -0.275 = -0.612882534 Simplifying x + -0.275 = -0.612882534 Reorder the terms: -0.275 + x = -0.612882534 Solving -0.275 + x = -0.612882534 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.275' to each side of the equation. -0.275 + 0.275 + x = -0.612882534 + 0.275 Combine like terms: -0.275 + 0.275 = 0.000 0.000 + x = -0.612882534 + 0.275 x = -0.612882534 + 0.275 Combine like terms: -0.612882534 + 0.275 = -0.337882534 x = -0.337882534 Simplifying x = -0.337882534Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.887882534, -0.337882534}
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