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Simplifying -2x2 + 9x = 5 Reorder the terms: 9x + -2x2 = 5 Solving 9x + -2x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 9x + -2x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -4.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -4.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -4.5x + x2 = 0 + -2.5 -4.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -4.5x + x2 = -2.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -2.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -2.5 + 5.0625 Combine like terms: -2.5 + 5.0625 = 2.5625 5.0625 + -4.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -2.25) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -2.25 = 1.600781059 Simplifying x + -2.25 = 1.600781059 Reorder the terms: -2.25 + x = 1.600781059 Solving -2.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.600781059 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.600781059 + 2.25 x = 1.600781059 + 2.25 Combine like terms: 1.600781059 + 2.25 = 3.850781059 x = 3.850781059 Simplifying x = 3.850781059Subproblem 2
x + -2.25 = -1.600781059 Simplifying x + -2.25 = -1.600781059 Reorder the terms: -2.25 + x = -1.600781059 Solving -2.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.600781059 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.600781059 + 2.25 x = -1.600781059 + 2.25 Combine like terms: -1.600781059 + 2.25 = 0.649218941 x = 0.649218941 Simplifying x = 0.649218941Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.850781059, 0.649218941}
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