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Simplifying x2 + -1x + -8 = 65 Reorder the terms: -8 + -1x + x2 = 65 Solving -8 + -1x + x2 = 65 Solving for variable 'x'. Reorder the terms: -8 + -65 + -1x + x2 = 65 + -65 Combine like terms: -8 + -65 = -73 -73 + -1x + x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -73 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + -1x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + -1x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + -1x + x2 = 0 + 73 -1x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 -1x + x2 = 73 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 73 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 73 + 0.25 Combine like terms: 73 + 0.25 = 73.25 0.25 + -1x + x2 = 73.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 73.25 Calculate the square root of the right side: 8.558621384 Break this problem into two subproblems by setting (x + -0.5) equal to 8.558621384 and -8.558621384.Subproblem 1
x + -0.5 = 8.558621384 Simplifying x + -0.5 = 8.558621384 Reorder the terms: -0.5 + x = 8.558621384 Solving -0.5 + x = 8.558621384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 8.558621384 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.558621384 + 0.5 x = 8.558621384 + 0.5 Combine like terms: 8.558621384 + 0.5 = 9.058621384 x = 9.058621384 Simplifying x = 9.058621384Subproblem 2
x + -0.5 = -8.558621384 Simplifying x + -0.5 = -8.558621384 Reorder the terms: -0.5 + x = -8.558621384 Solving -0.5 + x = -8.558621384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -8.558621384 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.558621384 + 0.5 x = -8.558621384 + 0.5 Combine like terms: -8.558621384 + 0.5 = -8.058621384 x = -8.058621384 Simplifying x = -8.058621384Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.058621384, -8.058621384}
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