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Simplifying x * x + 9x + -53 = 0 Multiply x * x x2 + 9x + -53 = 0 Reorder the terms: -53 + 9x + x2 = 0 Solving -53 + 9x + 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 + 9x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + 9x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 9x + x2 = 0 + 53 9x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 9x + x2 = 53 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 53 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 53 + 20.25 Combine like terms: 53 + 20.25 = 73.25 20.25 + 9x + x2 = 73.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 73.25 Calculate the square root of the right side: 8.558621384 Break this problem into two subproblems by setting (x + 4.5) equal to 8.558621384 and -8.558621384.Subproblem 1
x + 4.5 = 8.558621384 Simplifying x + 4.5 = 8.558621384 Reorder the terms: 4.5 + x = 8.558621384 Solving 4.5 + x = 8.558621384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 8.558621384 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 8.558621384 + -4.5 x = 8.558621384 + -4.5 Combine like terms: 8.558621384 + -4.5 = 4.058621384 x = 4.058621384 Simplifying x = 4.058621384Subproblem 2
x + 4.5 = -8.558621384 Simplifying x + 4.5 = -8.558621384 Reorder the terms: 4.5 + x = -8.558621384 Solving 4.5 + x = -8.558621384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -8.558621384 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -8.558621384 + -4.5 x = -8.558621384 + -4.5 Combine like terms: -8.558621384 + -4.5 = -13.058621384 x = -13.058621384 Simplifying x = -13.058621384Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.058621384, -13.058621384}
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