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Simplifying 25x2 = 60x + -26 Reorder the terms: 25x2 = -26 + 60x Solving 25x2 = -26 + 60x Solving for variable 'x'. Reorder the terms: 26 + -60x + 25x2 = -26 + 60x + 26 + -60x Reorder the terms: 26 + -60x + 25x2 = -26 + 26 + 60x + -60x Combine like terms: -26 + 26 = 0 26 + -60x + 25x2 = 0 + 60x + -60x 26 + -60x + 25x2 = 60x + -60x Combine like terms: 60x + -60x = 0 26 + -60x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1.04 + -2.4x + x2 = 0 Move the constant term to the right: Add '-1.04' to each side of the equation. 1.04 + -2.4x + -1.04 + x2 = 0 + -1.04 Reorder the terms: 1.04 + -1.04 + -2.4x + x2 = 0 + -1.04 Combine like terms: 1.04 + -1.04 = 0.00 0.00 + -2.4x + x2 = 0 + -1.04 -2.4x + x2 = 0 + -1.04 Combine like terms: 0 + -1.04 = -1.04 -2.4x + x2 = -1.04 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -1.04 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -1.04 + 1.44 Combine like terms: -1.04 + 1.44 = 0.4 1.44 + -2.4x + x2 = 0.4 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.4 Calculate the square root of the right side: 0.632455532 Break this problem into two subproblems by setting (x + -1.2) equal to 0.632455532 and -0.632455532.Subproblem 1
x + -1.2 = 0.632455532 Simplifying x + -1.2 = 0.632455532 Reorder the terms: -1.2 + x = 0.632455532 Solving -1.2 + x = 0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 0.632455532 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.632455532 + 1.2 x = 0.632455532 + 1.2 Combine like terms: 0.632455532 + 1.2 = 1.832455532 x = 1.832455532 Simplifying x = 1.832455532Subproblem 2
x + -1.2 = -0.632455532 Simplifying x + -1.2 = -0.632455532 Reorder the terms: -1.2 + x = -0.632455532 Solving -1.2 + x = -0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -0.632455532 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.632455532 + 1.2 x = -0.632455532 + 1.2 Combine like terms: -0.632455532 + 1.2 = 0.567544468 x = 0.567544468 Simplifying x = 0.567544468Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.832455532, 0.567544468}
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