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Simplifying 2x2 + 4.5x = 20 Reorder the terms: 4.5x + 2x2 = 20 Solving 4.5x + 2x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 4.5x + 2x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 4.5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + 2.25x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 2.25x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 2.25x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2.25x + x2 = 0 + 10 2.25x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 2.25x + x2 = 10 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 10 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 10 + 1.265625 Combine like terms: 10 + 1.265625 = 11.265625 1.265625 + 2.25x + x2 = 11.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 11.265625 Calculate the square root of the right side: 3.356430396 Break this problem into two subproblems by setting (x + 1.125) equal to 3.356430396 and -3.356430396.Subproblem 1
x + 1.125 = 3.356430396 Simplifying x + 1.125 = 3.356430396 Reorder the terms: 1.125 + x = 3.356430396 Solving 1.125 + x = 3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 3.356430396 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 3.356430396 + -1.125 x = 3.356430396 + -1.125 Combine like terms: 3.356430396 + -1.125 = 2.231430396 x = 2.231430396 Simplifying x = 2.231430396Subproblem 2
x + 1.125 = -3.356430396 Simplifying x + 1.125 = -3.356430396 Reorder the terms: 1.125 + x = -3.356430396 Solving 1.125 + x = -3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -3.356430396 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -3.356430396 + -1.125 x = -3.356430396 + -1.125 Combine like terms: -3.356430396 + -1.125 = -4.481430396 x = -4.481430396 Simplifying x = -4.481430396Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.231430396, -4.481430396}
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