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Simplifying 25x2 + -20x + -75 = 0 Reorder the terms: -75 + -20x + 25x2 = 0 Solving -75 + -20x + 25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-15 + -4x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-15 + -4x + 5x2)' equal to zero and attempt to solve: Simplifying -15 + -4x + 5x2 = 0 Solving -15 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + -0.8x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.8x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.8x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.8x + x2 = 0 + 3 -0.8x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.8x + x2 = 3 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 3 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 3 + 0.16 Combine like terms: 3 + 0.16 = 3.16 0.16 + -0.8x + x2 = 3.16 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 3.16 Calculate the square root of the right side: 1.777638883 Break this problem into two subproblems by setting (x + -0.4) equal to 1.777638883 and -1.777638883.Subproblem 1
x + -0.4 = 1.777638883 Simplifying x + -0.4 = 1.777638883 Reorder the terms: -0.4 + x = 1.777638883 Solving -0.4 + x = 1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.777638883 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.777638883 + 0.4 x = 1.777638883 + 0.4 Combine like terms: 1.777638883 + 0.4 = 2.177638883 x = 2.177638883 Simplifying x = 2.177638883Subproblem 2
x + -0.4 = -1.777638883 Simplifying x + -0.4 = -1.777638883 Reorder the terms: -0.4 + x = -1.777638883 Solving -0.4 + x = -1.777638883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.777638883 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.777638883 + 0.4 x = -1.777638883 + 0.4 Combine like terms: -1.777638883 + 0.4 = -1.377638883 x = -1.377638883 Simplifying x = -1.377638883Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.177638883, -1.377638883}Solution
x = {2.177638883, -1.377638883}
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