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Simplifying 25x2 + 115x + 75 = 0 Reorder the terms: 75 + 115x + 25x2 = 0 Solving 75 + 115x + 25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(15 + 23x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(15 + 23x + 5x2)' equal to zero and attempt to solve: Simplifying 15 + 23x + 5x2 = 0 Solving 15 + 23x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + 4.6x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 4.6x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 4.6x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4.6x + x2 = 0 + -3 4.6x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 4.6x + x2 = -3 The x term is 4.6x. Take half its coefficient (2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. 4.6x + 5.29 + x2 = -3 + 5.29 Reorder the terms: 5.29 + 4.6x + x2 = -3 + 5.29 Combine like terms: -3 + 5.29 = 2.29 5.29 + 4.6x + x2 = 2.29 Factor a perfect square on the left side: (x + 2.3)(x + 2.3) = 2.29 Calculate the square root of the right side: 1.513274595 Break this problem into two subproblems by setting (x + 2.3) equal to 1.513274595 and -1.513274595.Subproblem 1
x + 2.3 = 1.513274595 Simplifying x + 2.3 = 1.513274595 Reorder the terms: 2.3 + x = 1.513274595 Solving 2.3 + x = 1.513274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = 1.513274595 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = 1.513274595 + -2.3 x = 1.513274595 + -2.3 Combine like terms: 1.513274595 + -2.3 = -0.786725405 x = -0.786725405 Simplifying x = -0.786725405Subproblem 2
x + 2.3 = -1.513274595 Simplifying x + 2.3 = -1.513274595 Reorder the terms: 2.3 + x = -1.513274595 Solving 2.3 + x = -1.513274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + x = -1.513274595 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + x = -1.513274595 + -2.3 x = -1.513274595 + -2.3 Combine like terms: -1.513274595 + -2.3 = -3.813274595 x = -3.813274595 Simplifying x = -3.813274595Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.786725405, -3.813274595}Solution
x = {-0.786725405, -3.813274595}
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