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Simplifying 2x2 + 9x + -52 = 0 Reorder the terms: -52 + 9x + 2x2 = 0 Solving -52 + 9x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -26 + 4.5x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + 4.5x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 4.5x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 4.5x + x2 = 0 + 26 4.5x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 4.5x + x2 = 26 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 = 26 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 26 + 5.0625 Combine like terms: 26 + 5.0625 = 31.0625 5.0625 + 4.5x + x2 = 31.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 31.0625 Calculate the square root of the right side: 5.573374202 Break this problem into two subproblems by setting (x + 2.25) equal to 5.573374202 and -5.573374202.Subproblem 1
x + 2.25 = 5.573374202 Simplifying x + 2.25 = 5.573374202 Reorder the terms: 2.25 + x = 5.573374202 Solving 2.25 + x = 5.573374202 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 = 5.573374202 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 5.573374202 + -2.25 x = 5.573374202 + -2.25 Combine like terms: 5.573374202 + -2.25 = 3.323374202 x = 3.323374202 Simplifying x = 3.323374202Subproblem 2
x + 2.25 = -5.573374202 Simplifying x + 2.25 = -5.573374202 Reorder the terms: 2.25 + x = -5.573374202 Solving 2.25 + x = -5.573374202 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 = -5.573374202 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -5.573374202 + -2.25 x = -5.573374202 + -2.25 Combine like terms: -5.573374202 + -2.25 = -7.823374202 x = -7.823374202 Simplifying x = -7.823374202Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.323374202, -7.823374202}
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