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Simplifying 11x2 + -9x + -52 = 0 Reorder the terms: -52 + -9x + 11x2 = 0 Solving -52 + -9x + 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'. -4.727272727 + -0.8181818182x + x2 = 0 Move the constant term to the right: Add '4.727272727' to each side of the equation. -4.727272727 + -0.8181818182x + 4.727272727 + x2 = 0 + 4.727272727 Reorder the terms: -4.727272727 + 4.727272727 + -0.8181818182x + x2 = 0 + 4.727272727 Combine like terms: -4.727272727 + 4.727272727 = 0.000000000 0.000000000 + -0.8181818182x + x2 = 0 + 4.727272727 -0.8181818182x + x2 = 0 + 4.727272727 Combine like terms: 0 + 4.727272727 = 4.727272727 -0.8181818182x + x2 = 4.727272727 The x term is -0.8181818182x. Take half its coefficient (-0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. -0.8181818182x + 0.1673553719 + x2 = 4.727272727 + 0.1673553719 Reorder the terms: 0.1673553719 + -0.8181818182x + x2 = 4.727272727 + 0.1673553719 Combine like terms: 4.727272727 + 0.1673553719 = 4.8946280989 0.1673553719 + -0.8181818182x + x2 = 4.8946280989 Factor a perfect square on the left side: (x + -0.4090909091)(x + -0.4090909091) = 4.8946280989 Calculate the square root of the right side: 2.212380641 Break this problem into two subproblems by setting (x + -0.4090909091) equal to 2.212380641 and -2.212380641.Subproblem 1
x + -0.4090909091 = 2.212380641 Simplifying x + -0.4090909091 = 2.212380641 Reorder the terms: -0.4090909091 + x = 2.212380641 Solving -0.4090909091 + x = 2.212380641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + x = 2.212380641 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = 2.212380641 + 0.4090909091 x = 2.212380641 + 0.4090909091 Combine like terms: 2.212380641 + 0.4090909091 = 2.6214715501 x = 2.6214715501 Simplifying x = 2.6214715501Subproblem 2
x + -0.4090909091 = -2.212380641 Simplifying x + -0.4090909091 = -2.212380641 Reorder the terms: -0.4090909091 + x = -2.212380641 Solving -0.4090909091 + x = -2.212380641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + x = -2.212380641 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = -2.212380641 + 0.4090909091 x = -2.212380641 + 0.4090909091 Combine like terms: -2.212380641 + 0.4090909091 = -1.8032897319 x = -1.8032897319 Simplifying x = -1.8032897319Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6214715501, -1.8032897319}
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