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Simplifying x2 + -64x + 620 = 0 Reorder the terms: 620 + -64x + x2 = 0 Solving 620 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-620' to each side of the equation. 620 + -64x + -620 + x2 = 0 + -620 Reorder the terms: 620 + -620 + -64x + x2 = 0 + -620 Combine like terms: 620 + -620 = 0 0 + -64x + x2 = 0 + -620 -64x + x2 = 0 + -620 Combine like terms: 0 + -620 = -620 -64x + x2 = -620 The x term is -64x. Take half its coefficient (-32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. -64x + 1024 + x2 = -620 + 1024 Reorder the terms: 1024 + -64x + x2 = -620 + 1024 Combine like terms: -620 + 1024 = 404 1024 + -64x + x2 = 404 Factor a perfect square on the left side: (x + -32)(x + -32) = 404 Calculate the square root of the right side: 20.099751242 Break this problem into two subproblems by setting (x + -32) equal to 20.099751242 and -20.099751242.Subproblem 1
x + -32 = 20.099751242 Simplifying x + -32 = 20.099751242 Reorder the terms: -32 + x = 20.099751242 Solving -32 + x = 20.099751242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = 20.099751242 + 32 Combine like terms: -32 + 32 = 0 0 + x = 20.099751242 + 32 x = 20.099751242 + 32 Combine like terms: 20.099751242 + 32 = 52.099751242 x = 52.099751242 Simplifying x = 52.099751242Subproblem 2
x + -32 = -20.099751242 Simplifying x + -32 = -20.099751242 Reorder the terms: -32 + x = -20.099751242 Solving -32 + x = -20.099751242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = -20.099751242 + 32 Combine like terms: -32 + 32 = 0 0 + x = -20.099751242 + 32 x = -20.099751242 + 32 Combine like terms: -20.099751242 + 32 = 11.900248758 x = 11.900248758 Simplifying x = 11.900248758Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.099751242, 11.900248758}
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