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Simplifying x2 + 21x = 35 Reorder the terms: 21x + x2 = 35 Solving 21x + x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 21x + x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 21x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 21x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 21x + x2 = 0 + 35 21x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 21x + x2 = 35 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 = 35 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 35 + 110.25 Combine like terms: 35 + 110.25 = 145.25 110.25 + 21x + x2 = 145.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 145.25 Calculate the square root of the right side: 12.051970793 Break this problem into two subproblems by setting (x + 10.5) equal to 12.051970793 and -12.051970793.Subproblem 1
x + 10.5 = 12.051970793 Simplifying x + 10.5 = 12.051970793 Reorder the terms: 10.5 + x = 12.051970793 Solving 10.5 + x = 12.051970793 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 = 12.051970793 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 12.051970793 + -10.5 x = 12.051970793 + -10.5 Combine like terms: 12.051970793 + -10.5 = 1.551970793 x = 1.551970793 Simplifying x = 1.551970793Subproblem 2
x + 10.5 = -12.051970793 Simplifying x + 10.5 = -12.051970793 Reorder the terms: 10.5 + x = -12.051970793 Solving 10.5 + x = -12.051970793 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 = -12.051970793 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -12.051970793 + -10.5 x = -12.051970793 + -10.5 Combine like terms: -12.051970793 + -10.5 = -22.551970793 x = -22.551970793 Simplifying x = -22.551970793Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.551970793, -22.551970793}
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