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Simplifying x2 + 13x + -54 = 0 Reorder the terms: -54 + 13x + x2 = 0 Solving -54 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 13x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 13x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 13x + x2 = 0 + 54 13x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 13x + x2 = 54 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 = 54 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 54 + 42.25 Combine like terms: 54 + 42.25 = 96.25 42.25 + 13x + x2 = 96.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + 6.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + 6.5 = 9.810708435 Simplifying x + 6.5 = 9.810708435 Reorder the terms: 6.5 + x = 9.810708435 Solving 6.5 + x = 9.810708435 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 = 9.810708435 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 9.810708435 + -6.5 x = 9.810708435 + -6.5 Combine like terms: 9.810708435 + -6.5 = 3.310708435 x = 3.310708435 Simplifying x = 3.310708435Subproblem 2
x + 6.5 = -9.810708435 Simplifying x + 6.5 = -9.810708435 Reorder the terms: 6.5 + x = -9.810708435 Solving 6.5 + x = -9.810708435 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 = -9.810708435 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -9.810708435 + -6.5 x = -9.810708435 + -6.5 Combine like terms: -9.810708435 + -6.5 = -16.310708435 x = -16.310708435 Simplifying x = -16.310708435Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.310708435, -16.310708435}
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