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Simplifying -1x2 = 9x + 16 Reorder the terms: -1x2 = 16 + 9x Solving -1x2 = 16 + 9x Solving for variable 'x'. Reorder the terms: -16 + -9x + -1x2 = 16 + 9x + -16 + -9x Reorder the terms: -16 + -9x + -1x2 = 16 + -16 + 9x + -9x Combine like terms: 16 + -16 = 0 -16 + -9x + -1x2 = 0 + 9x + -9x -16 + -9x + -1x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -16 + -9x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 9x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 9x + x2)' equal to zero and attempt to solve: Simplifying 16 + 9x + x2 = 0 Solving 16 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 9x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 9x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 9x + x2 = 0 + -16 9x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 9x + x2 = -16 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 = -16 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -16 + 20.25 Combine like terms: -16 + 20.25 = 4.25 20.25 + 9x + x2 = 4.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 4.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 4.5 = 2.061552813 Simplifying x + 4.5 = 2.061552813 Reorder the terms: 4.5 + x = 2.061552813 Solving 4.5 + x = 2.061552813 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 = 2.061552813 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 2.061552813 + -4.5 x = 2.061552813 + -4.5 Combine like terms: 2.061552813 + -4.5 = -2.438447187 x = -2.438447187 Simplifying x = -2.438447187Subproblem 2
x + 4.5 = -2.061552813 Simplifying x + 4.5 = -2.061552813 Reorder the terms: 4.5 + x = -2.061552813 Solving 4.5 + x = -2.061552813 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 = -2.061552813 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -2.061552813 + -4.5 x = -2.061552813 + -4.5 Combine like terms: -2.061552813 + -4.5 = -6.561552813 x = -6.561552813 Simplifying x = -6.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.438447187, -6.561552813}Solution
x = {-2.438447187, -6.561552813}
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