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Simplifying 11x2 + -31x + -10 = 0 Reorder the terms: -10 + -31x + 11x2 = 0 Solving -10 + -31x + 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'. -0.9090909091 + -2.818181818x + x2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + -2.818181818x + 0.9090909091 + x2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + -2.818181818x + x2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + -2.818181818x + x2 = 0 + 0.9090909091 -2.818181818x + x2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 -2.818181818x + x2 = 0.9090909091 The x term is -2.818181818x. Take half its coefficient (-1.409090909). Square it (1.985537190) and add it to both sides. Add '1.985537190' to each side of the equation. -2.818181818x + 1.985537190 + x2 = 0.9090909091 + 1.985537190 Reorder the terms: 1.985537190 + -2.818181818x + x2 = 0.9090909091 + 1.985537190 Combine like terms: 0.9090909091 + 1.985537190 = 2.8946280991 1.985537190 + -2.818181818x + x2 = 2.8946280991 Factor a perfect square on the left side: (x + -1.409090909)(x + -1.409090909) = 2.8946280991 Calculate the square root of the right side: 1.701360661 Break this problem into two subproblems by setting (x + -1.409090909) equal to 1.701360661 and -1.701360661.Subproblem 1
x + -1.409090909 = 1.701360661 Simplifying x + -1.409090909 = 1.701360661 Reorder the terms: -1.409090909 + x = 1.701360661 Solving -1.409090909 + x = 1.701360661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.409090909' to each side of the equation. -1.409090909 + 1.409090909 + x = 1.701360661 + 1.409090909 Combine like terms: -1.409090909 + 1.409090909 = 0.000000000 0.000000000 + x = 1.701360661 + 1.409090909 x = 1.701360661 + 1.409090909 Combine like terms: 1.701360661 + 1.409090909 = 3.11045157 x = 3.11045157 Simplifying x = 3.11045157Subproblem 2
x + -1.409090909 = -1.701360661 Simplifying x + -1.409090909 = -1.701360661 Reorder the terms: -1.409090909 + x = -1.701360661 Solving -1.409090909 + x = -1.701360661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.409090909' to each side of the equation. -1.409090909 + 1.409090909 + x = -1.701360661 + 1.409090909 Combine like terms: -1.409090909 + 1.409090909 = 0.000000000 0.000000000 + x = -1.701360661 + 1.409090909 x = -1.701360661 + 1.409090909 Combine like terms: -1.701360661 + 1.409090909 = -0.292269752 x = -0.292269752 Simplifying x = -0.292269752Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.11045157, -0.292269752}
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