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Simplifying 5x(9 + 5x) = 169 (9 * 5x + 5x * 5x) = 169 (45x + 25x2) = 169 Solving 45x + 25x2 = 169 Solving for variable 'x'. Reorder the terms: -169 + 45x + 25x2 = 169 + -169 Combine like terms: 169 + -169 = 0 -169 + 45x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -6.76 + 1.8x + x2 = 0 Move the constant term to the right: Add '6.76' to each side of the equation. -6.76 + 1.8x + 6.76 + x2 = 0 + 6.76 Reorder the terms: -6.76 + 6.76 + 1.8x + x2 = 0 + 6.76 Combine like terms: -6.76 + 6.76 = 0.00 0.00 + 1.8x + x2 = 0 + 6.76 1.8x + x2 = 0 + 6.76 Combine like terms: 0 + 6.76 = 6.76 1.8x + x2 = 6.76 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 6.76 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 6.76 + 0.81 Combine like terms: 6.76 + 0.81 = 7.57 0.81 + 1.8x + x2 = 7.57 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 7.57 Calculate the square root of the right side: 2.751363298 Break this problem into two subproblems by setting (x + 0.9) equal to 2.751363298 and -2.751363298.Subproblem 1
x + 0.9 = 2.751363298 Simplifying x + 0.9 = 2.751363298 Reorder the terms: 0.9 + x = 2.751363298 Solving 0.9 + x = 2.751363298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 2.751363298 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 2.751363298 + -0.9 x = 2.751363298 + -0.9 Combine like terms: 2.751363298 + -0.9 = 1.851363298 x = 1.851363298 Simplifying x = 1.851363298Subproblem 2
x + 0.9 = -2.751363298 Simplifying x + 0.9 = -2.751363298 Reorder the terms: 0.9 + x = -2.751363298 Solving 0.9 + x = -2.751363298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -2.751363298 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -2.751363298 + -0.9 x = -2.751363298 + -0.9 Combine like terms: -2.751363298 + -0.9 = -3.651363298 x = -3.651363298 Simplifying x = -3.651363298Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.851363298, -3.651363298}
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