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Simplifying -11x2 + 36x + 45 = 0 Reorder the terms: 45 + 36x + -11x2 = 0 Solving 45 + 36x + -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'. -4.090909091 + -3.272727273x + x2 = 0 Move the constant term to the right: Add '4.090909091' to each side of the equation. -4.090909091 + -3.272727273x + 4.090909091 + x2 = 0 + 4.090909091 Reorder the terms: -4.090909091 + 4.090909091 + -3.272727273x + x2 = 0 + 4.090909091 Combine like terms: -4.090909091 + 4.090909091 = 0.000000000 0.000000000 + -3.272727273x + x2 = 0 + 4.090909091 -3.272727273x + x2 = 0 + 4.090909091 Combine like terms: 0 + 4.090909091 = 4.090909091 -3.272727273x + x2 = 4.090909091 The x term is -3.272727273x. Take half its coefficient (-1.636363637). Square it (2.677685953) and add it to both sides. Add '2.677685953' to each side of the equation. -3.272727273x + 2.677685953 + x2 = 4.090909091 + 2.677685953 Reorder the terms: 2.677685953 + -3.272727273x + x2 = 4.090909091 + 2.677685953 Combine like terms: 4.090909091 + 2.677685953 = 6.768595044 2.677685953 + -3.272727273x + x2 = 6.768595044 Factor a perfect square on the left side: (x + -1.636363637)(x + -1.636363637) = 6.768595044 Calculate the square root of the right side: 2.601652368 Break this problem into two subproblems by setting (x + -1.636363637) equal to 2.601652368 and -2.601652368.Subproblem 1
x + -1.636363637 = 2.601652368 Simplifying x + -1.636363637 = 2.601652368 Reorder the terms: -1.636363637 + x = 2.601652368 Solving -1.636363637 + x = 2.601652368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.636363637' to each side of the equation. -1.636363637 + 1.636363637 + x = 2.601652368 + 1.636363637 Combine like terms: -1.636363637 + 1.636363637 = 0.000000000 0.000000000 + x = 2.601652368 + 1.636363637 x = 2.601652368 + 1.636363637 Combine like terms: 2.601652368 + 1.636363637 = 4.238016005 x = 4.238016005 Simplifying x = 4.238016005Subproblem 2
x + -1.636363637 = -2.601652368 Simplifying x + -1.636363637 = -2.601652368 Reorder the terms: -1.636363637 + x = -2.601652368 Solving -1.636363637 + x = -2.601652368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.636363637' to each side of the equation. -1.636363637 + 1.636363637 + x = -2.601652368 + 1.636363637 Combine like terms: -1.636363637 + 1.636363637 = 0.000000000 0.000000000 + x = -2.601652368 + 1.636363637 x = -2.601652368 + 1.636363637 Combine like terms: -2.601652368 + 1.636363637 = -0.965288731 x = -0.965288731 Simplifying x = -0.965288731Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.238016005, -0.965288731}
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