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Simplifying 0 = 40 + -40x + 9x2 Solving 0 = 40 + -40x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + 40x + -9x2 = 40 + -40x + 9x2 + -40 + 40x + -9x2 Reorder the terms: -40 + 40x + -9x2 = 40 + -40 + -40x + 40x + 9x2 + -9x2 Combine like terms: 40 + -40 = 0 -40 + 40x + -9x2 = 0 + -40x + 40x + 9x2 + -9x2 -40 + 40x + -9x2 = -40x + 40x + 9x2 + -9x2 Combine like terms: -40x + 40x = 0 -40 + 40x + -9x2 = 0 + 9x2 + -9x2 -40 + 40x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -40 + 40x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 4.444444444 + -4.444444444x + x2 = 0 Move the constant term to the right: Add '-4.444444444' to each side of the equation. 4.444444444 + -4.444444444x + -4.444444444 + x2 = 0 + -4.444444444 Reorder the terms: 4.444444444 + -4.444444444 + -4.444444444x + x2 = 0 + -4.444444444 Combine like terms: 4.444444444 + -4.444444444 = 0.000000000 0.000000000 + -4.444444444x + x2 = 0 + -4.444444444 -4.444444444x + x2 = 0 + -4.444444444 Combine like terms: 0 + -4.444444444 = -4.444444444 -4.444444444x + x2 = -4.444444444 The x term is -4.444444444x. Take half its coefficient (-2.222222222). Square it (4.938271604) and add it to both sides. Add '4.938271604' to each side of the equation. -4.444444444x + 4.938271604 + x2 = -4.444444444 + 4.938271604 Reorder the terms: 4.938271604 + -4.444444444x + x2 = -4.444444444 + 4.938271604 Combine like terms: -4.444444444 + 4.938271604 = 0.49382716 4.938271604 + -4.444444444x + x2 = 0.49382716 Factor a perfect square on the left side: (x + -2.222222222)(x + -2.222222222) = 0.49382716 Calculate the square root of the right side: 0.702728369 Break this problem into two subproblems by setting (x + -2.222222222) equal to 0.702728369 and -0.702728369.Subproblem 1
x + -2.222222222 = 0.702728369 Simplifying x + -2.222222222 = 0.702728369 Reorder the terms: -2.222222222 + x = 0.702728369 Solving -2.222222222 + x = 0.702728369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = 0.702728369 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = 0.702728369 + 2.222222222 x = 0.702728369 + 2.222222222 Combine like terms: 0.702728369 + 2.222222222 = 2.924950591 x = 2.924950591 Simplifying x = 2.924950591Subproblem 2
x + -2.222222222 = -0.702728369 Simplifying x + -2.222222222 = -0.702728369 Reorder the terms: -2.222222222 + x = -0.702728369 Solving -2.222222222 + x = -0.702728369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = -0.702728369 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = -0.702728369 + 2.222222222 x = -0.702728369 + 2.222222222 Combine like terms: -0.702728369 + 2.222222222 = 1.519493853 x = 1.519493853 Simplifying x = 1.519493853Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.924950591, 1.519493853}
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