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Simplifying 25x2 + -24x + 3 = 0 Reorder the terms: 3 + -24x + 25x2 = 0 Solving 3 + -24x + 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'. 0.12 + -0.96x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -0.96x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -0.96x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -0.96x + x2 = 0 + -0.12 -0.96x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -0.96x + x2 = -0.12 The x term is -0.96x. Take half its coefficient (-0.48). Square it (0.2304) and add it to both sides. Add '0.2304' to each side of the equation. -0.96x + 0.2304 + x2 = -0.12 + 0.2304 Reorder the terms: 0.2304 + -0.96x + x2 = -0.12 + 0.2304 Combine like terms: -0.12 + 0.2304 = 0.1104 0.2304 + -0.96x + x2 = 0.1104 Factor a perfect square on the left side: (x + -0.48)(x + -0.48) = 0.1104 Calculate the square root of the right side: 0.332264955 Break this problem into two subproblems by setting (x + -0.48) equal to 0.332264955 and -0.332264955.Subproblem 1
x + -0.48 = 0.332264955 Simplifying x + -0.48 = 0.332264955 Reorder the terms: -0.48 + x = 0.332264955 Solving -0.48 + x = 0.332264955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.48' to each side of the equation. -0.48 + 0.48 + x = 0.332264955 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + x = 0.332264955 + 0.48 x = 0.332264955 + 0.48 Combine like terms: 0.332264955 + 0.48 = 0.812264955 x = 0.812264955 Simplifying x = 0.812264955Subproblem 2
x + -0.48 = -0.332264955 Simplifying x + -0.48 = -0.332264955 Reorder the terms: -0.48 + x = -0.332264955 Solving -0.48 + x = -0.332264955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.48' to each side of the equation. -0.48 + 0.48 + x = -0.332264955 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + x = -0.332264955 + 0.48 x = -0.332264955 + 0.48 Combine like terms: -0.332264955 + 0.48 = 0.147735045 x = 0.147735045 Simplifying x = 0.147735045Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.812264955, 0.147735045}
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