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Simplifying (x + -5)(x + -5) = 9x Reorder the terms: (-5 + x)(x + -5) = 9x Reorder the terms: (-5 + x)(-5 + x) = 9x Multiply (-5 + x) * (-5 + x) (-5(-5 + x) + x(-5 + x)) = 9x ((-5 * -5 + x * -5) + x(-5 + x)) = 9x ((25 + -5x) + x(-5 + x)) = 9x (25 + -5x + (-5 * x + x * x)) = 9x (25 + -5x + (-5x + x2)) = 9x Combine like terms: -5x + -5x = -10x (25 + -10x + x2) = 9x Solving 25 + -10x + x2 = 9x Solving for variable 'x'. Reorder the terms: 25 + -10x + -9x + x2 = 9x + -9x Combine like terms: -10x + -9x = -19x 25 + -19x + x2 = 9x + -9x Combine like terms: 9x + -9x = 0 25 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -19x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -19x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -19x + x2 = 0 + -25 -19x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -19x + x2 = -25 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -25 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -25 + 90.25 Combine like terms: -25 + 90.25 = 65.25 90.25 + -19x + x2 = 65.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + -9.5) equal to 8.077747211 and -8.077747211.Subproblem 1
x + -9.5 = 8.077747211 Simplifying x + -9.5 = 8.077747211 Reorder the terms: -9.5 + x = 8.077747211 Solving -9.5 + x = 8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 8.077747211 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 8.077747211 + 9.5 x = 8.077747211 + 9.5 Combine like terms: 8.077747211 + 9.5 = 17.577747211 x = 17.577747211 Simplifying x = 17.577747211Subproblem 2
x + -9.5 = -8.077747211 Simplifying x + -9.5 = -8.077747211 Reorder the terms: -9.5 + x = -8.077747211 Solving -9.5 + x = -8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -8.077747211 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -8.077747211 + 9.5 x = -8.077747211 + 9.5 Combine like terms: -8.077747211 + 9.5 = 1.422252789 x = 1.422252789 Simplifying x = 1.422252789Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.577747211, 1.422252789}
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