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Simplifying -11x2 + 7x + 3 = 0 Reorder the terms: 3 + 7x + -11x2 = 0 Solving 3 + 7x + -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'. -0.2727272727 + -0.6363636364x + x2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -0.6363636364x + 0.2727272727 + x2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -0.6363636364x + x2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -0.6363636364x + x2 = 0 + 0.2727272727 -0.6363636364x + x2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -0.6363636364x + x2 = 0.2727272727 The x term is -0.6363636364x. Take half its coefficient (-0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. -0.6363636364x + 0.1012396694 + x2 = 0.2727272727 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364x + x2 = 0.2727272727 + 0.1012396694 Combine like terms: 0.2727272727 + 0.1012396694 = 0.3739669421 0.1012396694 + -0.6363636364x + x2 = 0.3739669421 Factor a perfect square on the left side: (x + -0.3181818182)(x + -0.3181818182) = 0.3739669421 Calculate the square root of the right side: 0.611528366 Break this problem into two subproblems by setting (x + -0.3181818182) equal to 0.611528366 and -0.611528366.Subproblem 1
x + -0.3181818182 = 0.611528366 Simplifying x + -0.3181818182 = 0.611528366 Reorder the terms: -0.3181818182 + x = 0.611528366 Solving -0.3181818182 + x = 0.611528366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = 0.611528366 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = 0.611528366 + 0.3181818182 x = 0.611528366 + 0.3181818182 Combine like terms: 0.611528366 + 0.3181818182 = 0.9297101842 x = 0.9297101842 Simplifying x = 0.9297101842Subproblem 2
x + -0.3181818182 = -0.611528366 Simplifying x + -0.3181818182 = -0.611528366 Reorder the terms: -0.3181818182 + x = -0.611528366 Solving -0.3181818182 + x = -0.611528366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = -0.611528366 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = -0.611528366 + 0.3181818182 x = -0.611528366 + 0.3181818182 Combine like terms: -0.611528366 + 0.3181818182 = -0.2933465478 x = -0.2933465478 Simplifying x = -0.2933465478Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9297101842, -0.2933465478}
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