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Simplifying 11x(6x + -5) = 40 Reorder the terms: 11x(-5 + 6x) = 40 (-5 * 11x + 6x * 11x) = 40 (-55x + 66x2) = 40 Solving -55x + 66x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + -55x + 66x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -55x + 66x2 = 0 Begin completing the square. Divide all terms by 66 the coefficient of the squared term: Divide each side by '66'. -0.6060606061 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '0.6060606061' to each side of the equation. -0.6060606061 + -0.8333333333x + 0.6060606061 + x2 = 0 + 0.6060606061 Reorder the terms: -0.6060606061 + 0.6060606061 + -0.8333333333x + x2 = 0 + 0.6060606061 Combine like terms: -0.6060606061 + 0.6060606061 = 0.0000000000 0.0000000000 + -0.8333333333x + x2 = 0 + 0.6060606061 -0.8333333333x + x2 = 0 + 0.6060606061 Combine like terms: 0 + 0.6060606061 = 0.6060606061 -0.8333333333x + x2 = 0.6060606061 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = 0.6060606061 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 0.6060606061 + 0.1736111111 Combine like terms: 0.6060606061 + 0.1736111111 = 0.7796717172 0.1736111111 + -0.8333333333x + x2 = 0.7796717172 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 0.7796717172 Calculate the square root of the right side: 0.882990214 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 0.882990214 and -0.882990214.Subproblem 1
x + -0.4166666667 = 0.882990214 Simplifying x + -0.4166666667 = 0.882990214 Reorder the terms: -0.4166666667 + x = 0.882990214 Solving -0.4166666667 + x = 0.882990214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 0.882990214 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 0.882990214 + 0.4166666667 x = 0.882990214 + 0.4166666667 Combine like terms: 0.882990214 + 0.4166666667 = 1.2996568807 x = 1.2996568807 Simplifying x = 1.2996568807Subproblem 2
x + -0.4166666667 = -0.882990214 Simplifying x + -0.4166666667 = -0.882990214 Reorder the terms: -0.4166666667 + x = -0.882990214 Solving -0.4166666667 + x = -0.882990214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -0.882990214 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -0.882990214 + 0.4166666667 x = -0.882990214 + 0.4166666667 Combine like terms: -0.882990214 + 0.4166666667 = -0.4663235473 x = -0.4663235473 Simplifying x = -0.4663235473Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2996568807, -0.4663235473}
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