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Simplifying 0 = -1x2 + 21x + 11 Reorder the terms: 0 = 11 + 21x + -1x2 Solving 0 = 11 + 21x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + -21x + x2 = 11 + 21x + -1x2 + -11 + -21x + x2 Reorder the terms: -11 + -21x + x2 = 11 + -11 + 21x + -21x + -1x2 + x2 Combine like terms: 11 + -11 = 0 -11 + -21x + x2 = 0 + 21x + -21x + -1x2 + x2 -11 + -21x + x2 = 21x + -21x + -1x2 + x2 Combine like terms: 21x + -21x = 0 -11 + -21x + x2 = 0 + -1x2 + x2 -11 + -21x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -11 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -21x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -21x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -21x + x2 = 0 + 11 -21x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -21x + x2 = 11 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 11 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 11 + 110.25 Combine like terms: 11 + 110.25 = 121.25 110.25 + -21x + x2 = 121.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 121.25 Calculate the square root of the right side: 11.011357773 Break this problem into two subproblems by setting (x + -10.5) equal to 11.011357773 and -11.011357773.Subproblem 1
x + -10.5 = 11.011357773 Simplifying x + -10.5 = 11.011357773 Reorder the terms: -10.5 + x = 11.011357773 Solving -10.5 + x = 11.011357773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 11.011357773 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 11.011357773 + 10.5 x = 11.011357773 + 10.5 Combine like terms: 11.011357773 + 10.5 = 21.511357773 x = 21.511357773 Simplifying x = 21.511357773Subproblem 2
x + -10.5 = -11.011357773 Simplifying x + -10.5 = -11.011357773 Reorder the terms: -10.5 + x = -11.011357773 Solving -10.5 + x = -11.011357773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -11.011357773 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -11.011357773 + 10.5 x = -11.011357773 + 10.5 Combine like terms: -11.011357773 + 10.5 = -0.511357773 x = -0.511357773 Simplifying x = -0.511357773Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.511357773, -0.511357773}
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