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Simplifying x2 + 13x + 20 = 0 Reorder the terms: 20 + 13x + x2 = 0 Solving 20 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 13x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 13x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 13x + x2 = 0 + -20 13x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 13x + x2 = -20 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = -20 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -20 + 42.25 Combine like terms: -20 + 42.25 = 22.25 42.25 + 13x + x2 = 22.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + 6.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + 6.5 = 4.716990566 Simplifying x + 6.5 = 4.716990566 Reorder the terms: 6.5 + x = 4.716990566 Solving 6.5 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 4.716990566 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 4.716990566 + -6.5 x = 4.716990566 + -6.5 Combine like terms: 4.716990566 + -6.5 = -1.783009434 x = -1.783009434 Simplifying x = -1.783009434Subproblem 2
x + 6.5 = -4.716990566 Simplifying x + 6.5 = -4.716990566 Reorder the terms: 6.5 + x = -4.716990566 Solving 6.5 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -4.716990566 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -4.716990566 + -6.5 x = -4.716990566 + -6.5 Combine like terms: -4.716990566 + -6.5 = -11.216990566 x = -11.216990566 Simplifying x = -11.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.783009434, -11.216990566}
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