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Simplifying 2x2 + 9x = 10.125 Reorder the terms: 9x + 2x2 = 10.125 Solving 9x + 2x2 = 10.125 Solving for variable 'x'. Reorder the terms: -10.125 + 9x + 2x2 = 10.125 + -10.125 Combine like terms: 10.125 + -10.125 = 0.000 -10.125 + 9x + 2x2 = 0.000 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.0625 + 4.5x + x2 = 0.000 Move the constant term to the right: Add '5.0625' to each side of the equation. -5.0625 + 4.5x + 5.0625 + x2 = 0.000 + 5.0625 Reorder the terms: -5.0625 + 5.0625 + 4.5x + x2 = 0.000 + 5.0625 Combine like terms: -5.0625 + 5.0625 = 0.0000 0.0000 + 4.5x + x2 = 0.000 + 5.0625 4.5x + x2 = 0.000 + 5.0625 Combine like terms: 0.000 + 5.0625 = 5.0625 4.5x + x2 = 5.0625 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 = 5.0625 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 5.0625 + 5.0625 Combine like terms: 5.0625 + 5.0625 = 10.125 5.0625 + 4.5x + x2 = 10.125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 10.125 Calculate the square root of the right side: 3.181980515 Break this problem into two subproblems by setting (x + 2.25) equal to 3.181980515 and -3.181980515.Subproblem 1
x + 2.25 = 3.181980515 Simplifying x + 2.25 = 3.181980515 Reorder the terms: 2.25 + x = 3.181980515 Solving 2.25 + x = 3.181980515 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 = 3.181980515 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.181980515 + -2.25 x = 3.181980515 + -2.25 Combine like terms: 3.181980515 + -2.25 = 0.931980515 x = 0.931980515 Simplifying x = 0.931980515Subproblem 2
x + 2.25 = -3.181980515 Simplifying x + 2.25 = -3.181980515 Reorder the terms: 2.25 + x = -3.181980515 Solving 2.25 + x = -3.181980515 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 = -3.181980515 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.181980515 + -2.25 x = -3.181980515 + -2.25 Combine like terms: -3.181980515 + -2.25 = -5.431980515 x = -5.431980515 Simplifying x = -5.431980515Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.931980515, -5.431980515}
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