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Simplifying 4x2 + 10x + 25 = 300 Reorder the terms: 25 + 10x + 4x2 = 300 Solving 25 + 10x + 4x2 = 300 Solving for variable 'x'. Reorder the terms: 25 + -300 + 10x + 4x2 = 300 + -300 Combine like terms: 25 + -300 = -275 -275 + 10x + 4x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -275 + 10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -68.75 + 2.5x + x2 = 0 Move the constant term to the right: Add '68.75' to each side of the equation. -68.75 + 2.5x + 68.75 + x2 = 0 + 68.75 Reorder the terms: -68.75 + 68.75 + 2.5x + x2 = 0 + 68.75 Combine like terms: -68.75 + 68.75 = 0.00 0.00 + 2.5x + x2 = 0 + 68.75 2.5x + x2 = 0 + 68.75 Combine like terms: 0 + 68.75 = 68.75 2.5x + x2 = 68.75 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 68.75 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 68.75 + 1.5625 Combine like terms: 68.75 + 1.5625 = 70.3125 1.5625 + 2.5x + x2 = 70.3125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 70.3125 Calculate the square root of the right side: 8.385254916 Break this problem into two subproblems by setting (x + 1.25) equal to 8.385254916 and -8.385254916.Subproblem 1
x + 1.25 = 8.385254916 Simplifying x + 1.25 = 8.385254916 Reorder the terms: 1.25 + x = 8.385254916 Solving 1.25 + x = 8.385254916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 8.385254916 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 8.385254916 + -1.25 x = 8.385254916 + -1.25 Combine like terms: 8.385254916 + -1.25 = 7.135254916 x = 7.135254916 Simplifying x = 7.135254916Subproblem 2
x + 1.25 = -8.385254916 Simplifying x + 1.25 = -8.385254916 Reorder the terms: 1.25 + x = -8.385254916 Solving 1.25 + x = -8.385254916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -8.385254916 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -8.385254916 + -1.25 x = -8.385254916 + -1.25 Combine like terms: -8.385254916 + -1.25 = -9.635254916 x = -9.635254916 Simplifying x = -9.635254916Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.135254916, -9.635254916}
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