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Simplifying 9x2 + -85x = -9 Reorder the terms: -85x + 9x2 = -9 Solving -85x + 9x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + -85x + 9x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -85x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1 + -9.444444444x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -9.444444444x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -9.444444444x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9.444444444x + x2 = 0 + -1 -9.444444444x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -9.444444444x + x2 = -1 The x term is -9.444444444x. Take half its coefficient (-4.722222222). Square it (22.29938271) and add it to both sides. Add '22.29938271' to each side of the equation. -9.444444444x + 22.29938271 + x2 = -1 + 22.29938271 Reorder the terms: 22.29938271 + -9.444444444x + x2 = -1 + 22.29938271 Combine like terms: -1 + 22.29938271 = 21.29938271 22.29938271 + -9.444444444x + x2 = 21.29938271 Factor a perfect square on the left side: (x + -4.722222222)(x + -4.722222222) = 21.29938271 Calculate the square root of the right side: 4.615125427 Break this problem into two subproblems by setting (x + -4.722222222) equal to 4.615125427 and -4.615125427.Subproblem 1
x + -4.722222222 = 4.615125427 Simplifying x + -4.722222222 = 4.615125427 Reorder the terms: -4.722222222 + x = 4.615125427 Solving -4.722222222 + x = 4.615125427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.722222222' to each side of the equation. -4.722222222 + 4.722222222 + x = 4.615125427 + 4.722222222 Combine like terms: -4.722222222 + 4.722222222 = 0.000000000 0.000000000 + x = 4.615125427 + 4.722222222 x = 4.615125427 + 4.722222222 Combine like terms: 4.615125427 + 4.722222222 = 9.337347649 x = 9.337347649 Simplifying x = 9.337347649Subproblem 2
x + -4.722222222 = -4.615125427 Simplifying x + -4.722222222 = -4.615125427 Reorder the terms: -4.722222222 + x = -4.615125427 Solving -4.722222222 + x = -4.615125427 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.722222222' to each side of the equation. -4.722222222 + 4.722222222 + x = -4.615125427 + 4.722222222 Combine like terms: -4.722222222 + 4.722222222 = 0.000000000 0.000000000 + x = -4.615125427 + 4.722222222 x = -4.615125427 + 4.722222222 Combine like terms: -4.615125427 + 4.722222222 = 0.107096795 x = 0.107096795 Simplifying x = 0.107096795Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.337347649, 0.107096795}
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