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Simplifying 25x2 + -130x + 9 = 0 Reorder the terms: 9 + -130x + 25x2 = 0 Solving 9 + -130x + 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 + -5.2x + x2 = 0 Move the constant term to the right: Add '-0.36' to each side of the equation. 0.36 + -5.2x + -0.36 + x2 = 0 + -0.36 Reorder the terms: 0.36 + -0.36 + -5.2x + x2 = 0 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.00 + -5.2x + x2 = 0 + -0.36 -5.2x + x2 = 0 + -0.36 Combine like terms: 0 + -0.36 = -0.36 -5.2x + x2 = -0.36 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = -0.36 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = -0.36 + 6.76 Combine like terms: -0.36 + 6.76 = 6.4 6.76 + -5.2x + x2 = 6.4 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 6.4 Calculate the square root of the right side: 2.529822128 Break this problem into two subproblems by setting (x + -2.6) equal to 2.529822128 and -2.529822128.Subproblem 1
x + -2.6 = 2.529822128 Simplifying x + -2.6 = 2.529822128 Reorder the terms: -2.6 + x = 2.529822128 Solving -2.6 + x = 2.529822128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 2.529822128 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 2.529822128 + 2.6 x = 2.529822128 + 2.6 Combine like terms: 2.529822128 + 2.6 = 5.129822128 x = 5.129822128 Simplifying x = 5.129822128Subproblem 2
x + -2.6 = -2.529822128 Simplifying x + -2.6 = -2.529822128 Reorder the terms: -2.6 + x = -2.529822128 Solving -2.6 + x = -2.529822128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -2.529822128 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -2.529822128 + 2.6 x = -2.529822128 + 2.6 Combine like terms: -2.529822128 + 2.6 = 0.070177872 x = 0.070177872 Simplifying x = 0.070177872Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.129822128, 0.070177872}
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