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Simplifying x2 + -21x + -10 = 0 Reorder the terms: -10 + -21x + x2 = 0 Solving -10 + -21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -21x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -21x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -21x + x2 = 0 + 10 -21x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -21x + x2 = 10 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 = 10 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 10 + 110.25 Combine like terms: 10 + 110.25 = 120.25 110.25 + -21x + x2 = 120.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + -10.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + -10.5 = 10.9658561 Simplifying x + -10.5 = 10.9658561 Reorder the terms: -10.5 + x = 10.9658561 Solving -10.5 + x = 10.9658561 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 = 10.9658561 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 10.9658561 + 10.5 x = 10.9658561 + 10.5 Combine like terms: 10.9658561 + 10.5 = 21.4658561 x = 21.4658561 Simplifying x = 21.4658561Subproblem 2
x + -10.5 = -10.9658561 Simplifying x + -10.5 = -10.9658561 Reorder the terms: -10.5 + x = -10.9658561 Solving -10.5 + x = -10.9658561 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 = -10.9658561 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -10.9658561 + 10.5 x = -10.9658561 + 10.5 Combine like terms: -10.9658561 + 10.5 = -0.4658561 x = -0.4658561 Simplifying x = -0.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.4658561, -0.4658561}
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