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Simplifying (x2 + 5x + -528) = 0 Reorder the terms: (-528 + 5x + x2) = 0 Remove parenthesis around (-528 + 5x + x2) -528 + 5x + x2 = 0 Solving -528 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '528' to each side of the equation. -528 + 5x + 528 + x2 = 0 + 528 Reorder the terms: -528 + 528 + 5x + x2 = 0 + 528 Combine like terms: -528 + 528 = 0 0 + 5x + x2 = 0 + 528 5x + x2 = 0 + 528 Combine like terms: 0 + 528 = 528 5x + x2 = 528 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 = 528 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 528 + 6.25 Combine like terms: 528 + 6.25 = 534.25 6.25 + 5x + x2 = 534.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 534.25 Calculate the square root of the right side: 23.113848663 Break this problem into two subproblems by setting (x + 2.5) equal to 23.113848663 and -23.113848663.Subproblem 1
x + 2.5 = 23.113848663 Simplifying x + 2.5 = 23.113848663 Reorder the terms: 2.5 + x = 23.113848663 Solving 2.5 + x = 23.113848663 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 = 23.113848663 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 23.113848663 + -2.5 x = 23.113848663 + -2.5 Combine like terms: 23.113848663 + -2.5 = 20.613848663 x = 20.613848663 Simplifying x = 20.613848663Subproblem 2
x + 2.5 = -23.113848663 Simplifying x + 2.5 = -23.113848663 Reorder the terms: 2.5 + x = -23.113848663 Solving 2.5 + x = -23.113848663 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 = -23.113848663 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -23.113848663 + -2.5 x = -23.113848663 + -2.5 Combine like terms: -23.113848663 + -2.5 = -25.613848663 x = -25.613848663 Simplifying x = -25.613848663Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.613848663, -25.613848663}
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