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Simplifying 25x2 + -6x + 9 = 49 Reorder the terms: 9 + -6x + 25x2 = 49 Solving 9 + -6x + 25x2 = 49 Solving for variable 'x'. Reorder the terms: 9 + -49 + -6x + 25x2 = 49 + -49 Combine like terms: 9 + -49 = -40 -40 + -6x + 25x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -40 + -6x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.6 + -0.24x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -0.24x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -0.24x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -0.24x + x2 = 0 + 1.6 -0.24x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -0.24x + x2 = 1.6 The x term is -0.24x. Take half its coefficient (-0.12). Square it (0.0144) and add it to both sides. Add '0.0144' to each side of the equation. -0.24x + 0.0144 + x2 = 1.6 + 0.0144 Reorder the terms: 0.0144 + -0.24x + x2 = 1.6 + 0.0144 Combine like terms: 1.6 + 0.0144 = 1.6144 0.0144 + -0.24x + x2 = 1.6144 Factor a perfect square on the left side: (x + -0.12)(x + -0.12) = 1.6144 Calculate the square root of the right side: 1.270590414 Break this problem into two subproblems by setting (x + -0.12) equal to 1.270590414 and -1.270590414.Subproblem 1
x + -0.12 = 1.270590414 Simplifying x + -0.12 = 1.270590414 Reorder the terms: -0.12 + x = 1.270590414 Solving -0.12 + x = 1.270590414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.12' to each side of the equation. -0.12 + 0.12 + x = 1.270590414 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + x = 1.270590414 + 0.12 x = 1.270590414 + 0.12 Combine like terms: 1.270590414 + 0.12 = 1.390590414 x = 1.390590414 Simplifying x = 1.390590414Subproblem 2
x + -0.12 = -1.270590414 Simplifying x + -0.12 = -1.270590414 Reorder the terms: -0.12 + x = -1.270590414 Solving -0.12 + x = -1.270590414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.12' to each side of the equation. -0.12 + 0.12 + x = -1.270590414 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + x = -1.270590414 + 0.12 x = -1.270590414 + 0.12 Combine like terms: -1.270590414 + 0.12 = -1.150590414 x = -1.150590414 Simplifying x = -1.150590414Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.390590414, -1.150590414}
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