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Simplifying x2 + -9x + -130 = 0 Reorder the terms: -130 + -9x + x2 = 0 Solving -130 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + -9x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + -9x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + -9x + x2 = 0 + 130 -9x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 -9x + x2 = 130 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 = 130 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 130 + 20.25 Combine like terms: 130 + 20.25 = 150.25 20.25 + -9x + x2 = 150.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 150.25 Calculate the square root of the right side: 12.257650672 Break this problem into two subproblems by setting (x + -4.5) equal to 12.257650672 and -12.257650672.Subproblem 1
x + -4.5 = 12.257650672 Simplifying x + -4.5 = 12.257650672 Reorder the terms: -4.5 + x = 12.257650672 Solving -4.5 + x = 12.257650672 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 = 12.257650672 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 12.257650672 + 4.5 x = 12.257650672 + 4.5 Combine like terms: 12.257650672 + 4.5 = 16.757650672 x = 16.757650672 Simplifying x = 16.757650672Subproblem 2
x + -4.5 = -12.257650672 Simplifying x + -4.5 = -12.257650672 Reorder the terms: -4.5 + x = -12.257650672 Solving -4.5 + x = -12.257650672 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 = -12.257650672 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -12.257650672 + 4.5 x = -12.257650672 + 4.5 Combine like terms: -12.257650672 + 4.5 = -7.757650672 x = -7.757650672 Simplifying x = -7.757650672Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.757650672, -7.757650672}
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