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Simplifying x2 + 21x + -115 = 0 Reorder the terms: -115 + 21x + x2 = 0 Solving -115 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '115' to each side of the equation. -115 + 21x + 115 + x2 = 0 + 115 Reorder the terms: -115 + 115 + 21x + x2 = 0 + 115 Combine like terms: -115 + 115 = 0 0 + 21x + x2 = 0 + 115 21x + x2 = 0 + 115 Combine like terms: 0 + 115 = 115 21x + x2 = 115 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 = 115 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 115 + 110.25 Combine like terms: 115 + 110.25 = 225.25 110.25 + 21x + x2 = 225.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 225.25 Calculate the square root of the right side: 15.00833102 Break this problem into two subproblems by setting (x + 10.5) equal to 15.00833102 and -15.00833102.Subproblem 1
x + 10.5 = 15.00833102 Simplifying x + 10.5 = 15.00833102 Reorder the terms: 10.5 + x = 15.00833102 Solving 10.5 + x = 15.00833102 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 = 15.00833102 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 15.00833102 + -10.5 x = 15.00833102 + -10.5 Combine like terms: 15.00833102 + -10.5 = 4.50833102 x = 4.50833102 Simplifying x = 4.50833102Subproblem 2
x + 10.5 = -15.00833102 Simplifying x + 10.5 = -15.00833102 Reorder the terms: 10.5 + x = -15.00833102 Solving 10.5 + x = -15.00833102 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 = -15.00833102 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -15.00833102 + -10.5 x = -15.00833102 + -10.5 Combine like terms: -15.00833102 + -10.5 = -25.50833102 x = -25.50833102 Simplifying x = -25.50833102Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.50833102, -25.50833102}
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