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Simplifying 11z(z) + -1z = 3 Multiply z * z 11z2 + -1z = 3 Reorder the terms: -1z + 11z2 = 3 Solving -1z + 11z2 = 3 Solving for variable 'z'. Reorder the terms: -3 + -1z + 11z2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -1z + 11z2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.2727272727 + -0.09090909091z + z2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + -0.09090909091z + 0.2727272727 + z2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + -0.09090909091z + z2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + -0.09090909091z + z2 = 0 + 0.2727272727 -0.09090909091z + z2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 -0.09090909091z + z2 = 0.2727272727 The z term is -0.09090909091z. Take half its coefficient (-0.04545454546). Square it (0.002066115703) and add it to both sides. Add '0.002066115703' to each side of the equation. -0.09090909091z + 0.002066115703 + z2 = 0.2727272727 + 0.002066115703 Reorder the terms: 0.002066115703 + -0.09090909091z + z2 = 0.2727272727 + 0.002066115703 Combine like terms: 0.2727272727 + 0.002066115703 = 0.274793388403 0.002066115703 + -0.09090909091z + z2 = 0.274793388403 Factor a perfect square on the left side: (z + -0.04545454546)(z + -0.04545454546) = 0.274793388403 Calculate the square root of the right side: 0.524207391 Break this problem into two subproblems by setting (z + -0.04545454546) equal to 0.524207391 and -0.524207391.Subproblem 1
z + -0.04545454546 = 0.524207391 Simplifying z + -0.04545454546 = 0.524207391 Reorder the terms: -0.04545454546 + z = 0.524207391 Solving -0.04545454546 + z = 0.524207391 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + z = 0.524207391 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + z = 0.524207391 + 0.04545454546 z = 0.524207391 + 0.04545454546 Combine like terms: 0.524207391 + 0.04545454546 = 0.56966193646 z = 0.56966193646 Simplifying z = 0.56966193646Subproblem 2
z + -0.04545454546 = -0.524207391 Simplifying z + -0.04545454546 = -0.524207391 Reorder the terms: -0.04545454546 + z = -0.524207391 Solving -0.04545454546 + z = -0.524207391 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.04545454546' to each side of the equation. -0.04545454546 + 0.04545454546 + z = -0.524207391 + 0.04545454546 Combine like terms: -0.04545454546 + 0.04545454546 = 0.00000000000 0.00000000000 + z = -0.524207391 + 0.04545454546 z = -0.524207391 + 0.04545454546 Combine like terms: -0.524207391 + 0.04545454546 = -0.47875284554 z = -0.47875284554 Simplifying z = -0.47875284554Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.56966193646, -0.47875284554}
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