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Simplifying x2 + 5x + -53 = 0 Reorder the terms: -53 + 5x + x2 = 0 Solving -53 + 5x + 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 + 5x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + 5x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 5x + x2 = 0 + 53 5x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 5x + x2 = 53 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 53 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 53 + 6.25 Combine like terms: 53 + 6.25 = 59.25 6.25 + 5x + x2 = 59.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 59.25 Calculate the square root of the right side: 7.697402159 Break this problem into two subproblems by setting (x + 2.5) equal to 7.697402159 and -7.697402159.Subproblem 1
x + 2.5 = 7.697402159 Simplifying x + 2.5 = 7.697402159 Reorder the terms: 2.5 + x = 7.697402159 Solving 2.5 + x = 7.697402159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 7.697402159 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.697402159 + -2.5 x = 7.697402159 + -2.5 Combine like terms: 7.697402159 + -2.5 = 5.197402159 x = 5.197402159 Simplifying x = 5.197402159Subproblem 2
x + 2.5 = -7.697402159 Simplifying x + 2.5 = -7.697402159 Reorder the terms: 2.5 + x = -7.697402159 Solving 2.5 + x = -7.697402159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -7.697402159 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.697402159 + -2.5 x = -7.697402159 + -2.5 Combine like terms: -7.697402159 + -2.5 = -10.197402159 x = -10.197402159 Simplifying x = -10.197402159Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.197402159, -10.197402159}
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