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Simplifying x2 + -61x + 450 = 0 Reorder the terms: 450 + -61x + x2 = 0 Solving 450 + -61x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-450' to each side of the equation. 450 + -61x + -450 + x2 = 0 + -450 Reorder the terms: 450 + -450 + -61x + x2 = 0 + -450 Combine like terms: 450 + -450 = 0 0 + -61x + x2 = 0 + -450 -61x + x2 = 0 + -450 Combine like terms: 0 + -450 = -450 -61x + x2 = -450 The x term is -61x. Take half its coefficient (-30.5). Square it (930.25) and add it to both sides. Add '930.25' to each side of the equation. -61x + 930.25 + x2 = -450 + 930.25 Reorder the terms: 930.25 + -61x + x2 = -450 + 930.25 Combine like terms: -450 + 930.25 = 480.25 930.25 + -61x + x2 = 480.25 Factor a perfect square on the left side: (x + -30.5)(x + -30.5) = 480.25 Calculate the square root of the right side: 21.914607001 Break this problem into two subproblems by setting (x + -30.5) equal to 21.914607001 and -21.914607001.Subproblem 1
x + -30.5 = 21.914607001 Simplifying x + -30.5 = 21.914607001 Reorder the terms: -30.5 + x = 21.914607001 Solving -30.5 + x = 21.914607001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.5' to each side of the equation. -30.5 + 30.5 + x = 21.914607001 + 30.5 Combine like terms: -30.5 + 30.5 = 0.0 0.0 + x = 21.914607001 + 30.5 x = 21.914607001 + 30.5 Combine like terms: 21.914607001 + 30.5 = 52.414607001 x = 52.414607001 Simplifying x = 52.414607001Subproblem 2
x + -30.5 = -21.914607001 Simplifying x + -30.5 = -21.914607001 Reorder the terms: -30.5 + x = -21.914607001 Solving -30.5 + x = -21.914607001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.5' to each side of the equation. -30.5 + 30.5 + x = -21.914607001 + 30.5 Combine like terms: -30.5 + 30.5 = 0.0 0.0 + x = -21.914607001 + 30.5 x = -21.914607001 + 30.5 Combine like terms: -21.914607001 + 30.5 = 8.585392999 x = 8.585392999 Simplifying x = 8.585392999Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.414607001, 8.585392999}
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