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Simplifying x2 + 13x = 53 Reorder the terms: 13x + x2 = 53 Solving 13x + x2 = 53 Solving for variable 'x'. Reorder the terms: -53 + 13x + x2 = 53 + -53 Combine like terms: 53 + -53 = 0 -53 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + 13x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + 13x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 13x + x2 = 0 + 53 13x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 13x + x2 = 53 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 = 53 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 53 + 42.25 Combine like terms: 53 + 42.25 = 95.25 42.25 + 13x + x2 = 95.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 95.25 Calculate the square root of the right side: 9.759610648 Break this problem into two subproblems by setting (x + 6.5) equal to 9.759610648 and -9.759610648.Subproblem 1
x + 6.5 = 9.759610648 Simplifying x + 6.5 = 9.759610648 Reorder the terms: 6.5 + x = 9.759610648 Solving 6.5 + x = 9.759610648 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 = 9.759610648 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 9.759610648 + -6.5 x = 9.759610648 + -6.5 Combine like terms: 9.759610648 + -6.5 = 3.259610648 x = 3.259610648 Simplifying x = 3.259610648Subproblem 2
x + 6.5 = -9.759610648 Simplifying x + 6.5 = -9.759610648 Reorder the terms: 6.5 + x = -9.759610648 Solving 6.5 + x = -9.759610648 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 = -9.759610648 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -9.759610648 + -6.5 x = -9.759610648 + -6.5 Combine like terms: -9.759610648 + -6.5 = -16.259610648 x = -16.259610648 Simplifying x = -16.259610648Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.259610648, -16.259610648}
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