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Simplifying 25x2 + 24x + -9 = 0 Reorder the terms: -9 + 24x + 25x2 = 0 Solving -9 + 24x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.36 + 0.96x + x2 = 0 Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + 0.96x + 0.36 + x2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + 0.96x + x2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + 0.96x + x2 = 0 + 0.36 0.96x + x2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 0.96x + x2 = 0.36 The x term is 0.96x. Take half its coefficient (0.48). Square it (0.2304) and add it to both sides. Add '0.2304' to each side of the equation. 0.96x + 0.2304 + x2 = 0.36 + 0.2304 Reorder the terms: 0.2304 + 0.96x + x2 = 0.36 + 0.2304 Combine like terms: 0.36 + 0.2304 = 0.5904 0.2304 + 0.96x + x2 = 0.5904 Factor a perfect square on the left side: (x + 0.48)(x + 0.48) = 0.5904 Calculate the square root of the right side: 0.768374908 Break this problem into two subproblems by setting (x + 0.48) equal to 0.768374908 and -0.768374908.Subproblem 1
x + 0.48 = 0.768374908 Simplifying x + 0.48 = 0.768374908 Reorder the terms: 0.48 + x = 0.768374908 Solving 0.48 + x = 0.768374908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.48' to each side of the equation. 0.48 + -0.48 + x = 0.768374908 + -0.48 Combine like terms: 0.48 + -0.48 = 0.00 0.00 + x = 0.768374908 + -0.48 x = 0.768374908 + -0.48 Combine like terms: 0.768374908 + -0.48 = 0.288374908 x = 0.288374908 Simplifying x = 0.288374908Subproblem 2
x + 0.48 = -0.768374908 Simplifying x + 0.48 = -0.768374908 Reorder the terms: 0.48 + x = -0.768374908 Solving 0.48 + x = -0.768374908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.48' to each side of the equation. 0.48 + -0.48 + x = -0.768374908 + -0.48 Combine like terms: 0.48 + -0.48 = 0.00 0.00 + x = -0.768374908 + -0.48 x = -0.768374908 + -0.48 Combine like terms: -0.768374908 + -0.48 = -1.248374908 x = -1.248374908 Simplifying x = -1.248374908Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.288374908, -1.248374908}
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