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Simplifying x2 + 21x + -110 = 0 Reorder the terms: -110 + 21x + x2 = 0 Solving -110 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 21x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 21x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 21x + x2 = 0 + 110 21x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 21x + x2 = 110 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 = 110 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 110 + 110.25 Combine like terms: 110 + 110.25 = 220.25 110.25 + 21x + x2 = 220.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 220.25 Calculate the square root of the right side: 14.84082208 Break this problem into two subproblems by setting (x + 10.5) equal to 14.84082208 and -14.84082208.Subproblem 1
x + 10.5 = 14.84082208 Simplifying x + 10.5 = 14.84082208 Reorder the terms: 10.5 + x = 14.84082208 Solving 10.5 + x = 14.84082208 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 = 14.84082208 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 14.84082208 + -10.5 x = 14.84082208 + -10.5 Combine like terms: 14.84082208 + -10.5 = 4.34082208 x = 4.34082208 Simplifying x = 4.34082208Subproblem 2
x + 10.5 = -14.84082208 Simplifying x + 10.5 = -14.84082208 Reorder the terms: 10.5 + x = -14.84082208 Solving 10.5 + x = -14.84082208 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 = -14.84082208 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -14.84082208 + -10.5 x = -14.84082208 + -10.5 Combine like terms: -14.84082208 + -10.5 = -25.34082208 x = -25.34082208 Simplifying x = -25.34082208Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.34082208, -25.34082208}
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