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Simplifying -11x2 + 15x + 4 = 0 Reorder the terms: 4 + 15x + -11x2 = 0 Solving 4 + 15x + -11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.3636363636 + -1.363636364x + x2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + -1.363636364x + 0.3636363636 + x2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + -1.363636364x + x2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + -1.363636364x + x2 = 0 + 0.3636363636 -1.363636364x + x2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 -1.363636364x + x2 = 0.3636363636 The x term is -1.363636364x. Take half its coefficient (-0.681818182). Square it (0.4648760333) and add it to both sides. Add '0.4648760333' to each side of the equation. -1.363636364x + 0.4648760333 + x2 = 0.3636363636 + 0.4648760333 Reorder the terms: 0.4648760333 + -1.363636364x + x2 = 0.3636363636 + 0.4648760333 Combine like terms: 0.3636363636 + 0.4648760333 = 0.8285123969 0.4648760333 + -1.363636364x + x2 = 0.8285123969 Factor a perfect square on the left side: (x + -0.681818182)(x + -0.681818182) = 0.8285123969 Calculate the square root of the right side: 0.910226564 Break this problem into two subproblems by setting (x + -0.681818182) equal to 0.910226564 and -0.910226564.Subproblem 1
x + -0.681818182 = 0.910226564 Simplifying x + -0.681818182 = 0.910226564 Reorder the terms: -0.681818182 + x = 0.910226564 Solving -0.681818182 + x = 0.910226564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.681818182' to each side of the equation. -0.681818182 + 0.681818182 + x = 0.910226564 + 0.681818182 Combine like terms: -0.681818182 + 0.681818182 = 0.000000000 0.000000000 + x = 0.910226564 + 0.681818182 x = 0.910226564 + 0.681818182 Combine like terms: 0.910226564 + 0.681818182 = 1.592044746 x = 1.592044746 Simplifying x = 1.592044746Subproblem 2
x + -0.681818182 = -0.910226564 Simplifying x + -0.681818182 = -0.910226564 Reorder the terms: -0.681818182 + x = -0.910226564 Solving -0.681818182 + x = -0.910226564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.681818182' to each side of the equation. -0.681818182 + 0.681818182 + x = -0.910226564 + 0.681818182 Combine like terms: -0.681818182 + 0.681818182 = 0.000000000 0.000000000 + x = -0.910226564 + 0.681818182 x = -0.910226564 + 0.681818182 Combine like terms: -0.910226564 + 0.681818182 = -0.228408382 x = -0.228408382 Simplifying x = -0.228408382Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.592044746, -0.228408382}
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