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Simplifying X2 + -21X + -90 = 0 Reorder the terms: -90 + -21X + X2 = 0 Solving -90 + -21X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -21X + 90 + X2 = 0 + 90 Reorder the terms: -90 + 90 + -21X + X2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -21X + X2 = 0 + 90 -21X + X2 = 0 + 90 Combine like terms: 0 + 90 = 90 -21X + X2 = 90 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 = 90 + 110.25 Reorder the terms: 110.25 + -21X + X2 = 90 + 110.25 Combine like terms: 90 + 110.25 = 200.25 110.25 + -21X + X2 = 200.25 Factor a perfect square on the left side: (X + -10.5)(X + -10.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (X + -10.5) equal to 14.150971698 and -14.150971698.Subproblem 1
X + -10.5 = 14.150971698 Simplifying X + -10.5 = 14.150971698 Reorder the terms: -10.5 + X = 14.150971698 Solving -10.5 + X = 14.150971698 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 = 14.150971698 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + X = 14.150971698 + 10.5 X = 14.150971698 + 10.5 Combine like terms: 14.150971698 + 10.5 = 24.650971698 X = 24.650971698 Simplifying X = 24.650971698Subproblem 2
X + -10.5 = -14.150971698 Simplifying X + -10.5 = -14.150971698 Reorder the terms: -10.5 + X = -14.150971698 Solving -10.5 + X = -14.150971698 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 = -14.150971698 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + X = -14.150971698 + 10.5 X = -14.150971698 + 10.5 Combine like terms: -14.150971698 + 10.5 = -3.650971698 X = -3.650971698 Simplifying X = -3.650971698Solution
The solution to the problem is based on the solutions from the subproblems. X = {24.650971698, -3.650971698}
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