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Simplifying 5x2 + 15x + 5.25 = 0 Reorder the terms: 5.25 + 15x + 5x2 = 0 Solving 5.25 + 15x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.05 + 3x + x2 = 0 Move the constant term to the right: Add '-1.05' to each side of the equation. 1.05 + 3x + -1.05 + x2 = 0 + -1.05 Reorder the terms: 1.05 + -1.05 + 3x + x2 = 0 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + 3x + x2 = 0 + -1.05 3x + x2 = 0 + -1.05 Combine like terms: 0 + -1.05 = -1.05 3x + x2 = -1.05 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -1.05 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -1.05 + 2.25 Combine like terms: -1.05 + 2.25 = 1.2 2.25 + 3x + x2 = 1.2 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (x + 1.5) equal to 1.095445115 and -1.095445115.Subproblem 1
x + 1.5 = 1.095445115 Simplifying x + 1.5 = 1.095445115 Reorder the terms: 1.5 + x = 1.095445115 Solving 1.5 + x = 1.095445115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.095445115 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.095445115 + -1.5 x = 1.095445115 + -1.5 Combine like terms: 1.095445115 + -1.5 = -0.404554885 x = -0.404554885 Simplifying x = -0.404554885Subproblem 2
x + 1.5 = -1.095445115 Simplifying x + 1.5 = -1.095445115 Reorder the terms: 1.5 + x = -1.095445115 Solving 1.5 + x = -1.095445115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.095445115 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.095445115 + -1.5 x = -1.095445115 + -1.5 Combine like terms: -1.095445115 + -1.5 = -2.595445115 x = -2.595445115 Simplifying x = -2.595445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.404554885, -2.595445115}
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