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Simplifying 25x2 + 25x + -130 = 0 Reorder the terms: -130 + 25x + 25x2 = 0 Solving -130 + 25x + 25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-26 + 5x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-26 + 5x + 5x2)' equal to zero and attempt to solve: Simplifying -26 + 5x + 5x2 = 0 Solving -26 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.2 + x + x2 = 0 Move the constant term to the right: Add '5.2' to each side of the equation. -5.2 + x + 5.2 + x2 = 0 + 5.2 Reorder the terms: -5.2 + 5.2 + x + x2 = 0 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + x + x2 = 0 + 5.2 x + x2 = 0 + 5.2 Combine like terms: 0 + 5.2 = 5.2 x + x2 = 5.2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 5.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 5.2 + 0.25 Combine like terms: 5.2 + 0.25 = 5.45 1.25 + x2 = 5.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.45 Calculate the square root of the right side: 2.334523506 Break this problem into two subproblems by setting (x + 0.5) equal to 2.334523506 and -2.334523506.Subproblem 1
x + 0.5 = 2.334523506 Simplifying x + 0.5 = 2.334523506 Reorder the terms: 0.5 + x = 2.334523506 Solving 0.5 + x = 2.334523506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.334523506 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.334523506 + -0.5 x = 2.334523506 + -0.5 Combine like terms: 2.334523506 + -0.5 = 1.834523506 x = 1.834523506 Simplifying x = 1.834523506Subproblem 2
x + 0.5 = -2.334523506 Simplifying x + 0.5 = -2.334523506 Reorder the terms: 0.5 + x = -2.334523506 Solving 0.5 + x = -2.334523506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.334523506 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.334523506 + -0.5 x = -2.334523506 + -0.5 Combine like terms: -2.334523506 + -0.5 = -2.834523506 x = -2.834523506 Simplifying x = -2.834523506Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.834523506, -2.834523506}Solution
x = {1.834523506, -2.834523506}
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