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Simplifying x2 + 23x + 53 = 0 Reorder the terms: 53 + 23x + x2 = 0 Solving 53 + 23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 23x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + 23x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 23x + x2 = 0 + -53 23x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 23x + x2 = -53 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = -53 + 132.25 Reorder the terms: 132.25 + 23x + x2 = -53 + 132.25 Combine like terms: -53 + 132.25 = 79.25 132.25 + 23x + x2 = 79.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 79.25 Calculate the square root of the right side: 8.902246907 Break this problem into two subproblems by setting (x + 11.5) equal to 8.902246907 and -8.902246907.Subproblem 1
x + 11.5 = 8.902246907 Simplifying x + 11.5 = 8.902246907 Reorder the terms: 11.5 + x = 8.902246907 Solving 11.5 + x = 8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 8.902246907 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 8.902246907 + -11.5 x = 8.902246907 + -11.5 Combine like terms: 8.902246907 + -11.5 = -2.597753093 x = -2.597753093 Simplifying x = -2.597753093Subproblem 2
x + 11.5 = -8.902246907 Simplifying x + 11.5 = -8.902246907 Reorder the terms: 11.5 + x = -8.902246907 Solving 11.5 + x = -8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -8.902246907 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -8.902246907 + -11.5 x = -8.902246907 + -11.5 Combine like terms: -8.902246907 + -11.5 = -20.402246907 x = -20.402246907 Simplifying x = -20.402246907Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.597753093, -20.402246907}
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