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Simplifying x2 + -4x = 5x + 35 Reorder the terms: -4x + x2 = 5x + 35 Reorder the terms: -4x + x2 = 35 + 5x Solving -4x + x2 = 35 + 5x Solving for variable 'x'. Reorder the terms: -35 + -4x + -5x + x2 = 35 + 5x + -35 + -5x Combine like terms: -4x + -5x = -9x -35 + -9x + x2 = 35 + 5x + -35 + -5x Reorder the terms: -35 + -9x + x2 = 35 + -35 + 5x + -5x Combine like terms: 35 + -35 = 0 -35 + -9x + x2 = 0 + 5x + -5x -35 + -9x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -35 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -9x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -9x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -9x + x2 = 0 + 35 -9x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -9x + x2 = 35 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 = 35 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 35 + 20.25 Combine like terms: 35 + 20.25 = 55.25 20.25 + -9x + x2 = 55.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + -4.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + -4.5 = 7.433034374 Simplifying x + -4.5 = 7.433034374 Reorder the terms: -4.5 + x = 7.433034374 Solving -4.5 + x = 7.433034374 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 = 7.433034374 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 7.433034374 + 4.5 x = 7.433034374 + 4.5 Combine like terms: 7.433034374 + 4.5 = 11.933034374 x = 11.933034374 Simplifying x = 11.933034374Subproblem 2
x + -4.5 = -7.433034374 Simplifying x + -4.5 = -7.433034374 Reorder the terms: -4.5 + x = -7.433034374 Solving -4.5 + x = -7.433034374 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 = -7.433034374 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -7.433034374 + 4.5 x = -7.433034374 + 4.5 Combine like terms: -7.433034374 + 4.5 = -2.933034374 x = -2.933034374 Simplifying x = -2.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.933034374, -2.933034374}
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