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Simplifying 25x2 + -60x + 25 = 0 Reorder the terms: 25 + -60x + 25x2 = 0 Solving 25 + -60x + 25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(5 + -12x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + -12x + 5x2)' equal to zero and attempt to solve: Simplifying 5 + -12x + 5x2 = 0 Solving 5 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + -2.4x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.4x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.4x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.4x + x2 = 0 + -1 -2.4x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.4x + x2 = -1 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 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -1 + 1.44 Combine like terms: -1 + 1.44 = 0.44 1.44 + -2.4x + x2 = 0.44 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (x + -1.2) equal to 0.663324958 and -0.663324958.Subproblem 1
x + -1.2 = 0.663324958 Simplifying x + -1.2 = 0.663324958 Reorder the terms: -1.2 + x = 0.663324958 Solving -1.2 + x = 0.663324958 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 = 0.663324958 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.663324958 + 1.2 x = 0.663324958 + 1.2 Combine like terms: 0.663324958 + 1.2 = 1.863324958 x = 1.863324958 Simplifying x = 1.863324958Subproblem 2
x + -1.2 = -0.663324958 Simplifying x + -1.2 = -0.663324958 Reorder the terms: -1.2 + x = -0.663324958 Solving -1.2 + x = -0.663324958 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 = -0.663324958 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.663324958 + 1.2 x = -0.663324958 + 1.2 Combine like terms: -0.663324958 + 1.2 = 0.536675042 x = 0.536675042 Simplifying x = 0.536675042Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.863324958, 0.536675042}Solution
x = {1.863324958, 0.536675042}
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