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Simplifying (x + 9)(x + -9) = x Reorder the terms: (9 + x)(x + -9) = x Reorder the terms: (9 + x)(-9 + x) = x Multiply (9 + x) * (-9 + x) (9(-9 + x) + x(-9 + x)) = x ((-9 * 9 + x * 9) + x(-9 + x)) = x ((-81 + 9x) + x(-9 + x)) = x (-81 + 9x + (-9 * x + x * x)) = x (-81 + 9x + (-9x + x2)) = x Combine like terms: 9x + -9x = 0 (-81 + 0 + x2) = x (-81 + x2) = x Solving -81 + x2 = x Solving for variable 'x'. Reorder the terms: -81 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -81 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -1x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + -1x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -1x + x2 = 0 + 81 -1x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 -1x + x2 = 81 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 = 81 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 81 + 0.25 Combine like terms: 81 + 0.25 = 81.25 0.25 + -1x + x2 = 81.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + -0.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + -0.5 = 9.013878189 Simplifying x + -0.5 = 9.013878189 Reorder the terms: -0.5 + x = 9.013878189 Solving -0.5 + x = 9.013878189 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 = 9.013878189 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 9.013878189 + 0.5 x = 9.013878189 + 0.5 Combine like terms: 9.013878189 + 0.5 = 9.513878189 x = 9.513878189 Simplifying x = 9.513878189Subproblem 2
x + -0.5 = -9.013878189 Simplifying x + -0.5 = -9.013878189 Reorder the terms: -0.5 + x = -9.013878189 Solving -0.5 + x = -9.013878189 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 = -9.013878189 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -9.013878189 + 0.5 x = -9.013878189 + 0.5 Combine like terms: -9.013878189 + 0.5 = -8.513878189 x = -8.513878189 Simplifying x = -8.513878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.513878189, -8.513878189}
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