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Simplifying 2x2 + 9x = 25 Reorder the terms: 9x + 2x2 = 25 Solving 9x + 2x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 9x + 2x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 4.5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 4.5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 4.5x + x2 = 0 + 12.5 4.5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 4.5x + x2 = 12.5 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 = 12.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 12.5 + 5.0625 Combine like terms: 12.5 + 5.0625 = 17.5625 5.0625 + 4.5x + x2 = 17.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 17.5625 Calculate the square root of the right side: 4.190763654 Break this problem into two subproblems by setting (x + 2.25) equal to 4.190763654 and -4.190763654.Subproblem 1
x + 2.25 = 4.190763654 Simplifying x + 2.25 = 4.190763654 Reorder the terms: 2.25 + x = 4.190763654 Solving 2.25 + x = 4.190763654 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 = 4.190763654 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 4.190763654 + -2.25 x = 4.190763654 + -2.25 Combine like terms: 4.190763654 + -2.25 = 1.940763654 x = 1.940763654 Simplifying x = 1.940763654Subproblem 2
x + 2.25 = -4.190763654 Simplifying x + 2.25 = -4.190763654 Reorder the terms: 2.25 + x = -4.190763654 Solving 2.25 + x = -4.190763654 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 = -4.190763654 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -4.190763654 + -2.25 x = -4.190763654 + -2.25 Combine like terms: -4.190763654 + -2.25 = -6.440763654 x = -6.440763654 Simplifying x = -6.440763654Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.940763654, -6.440763654}
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