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Simplifying -20x2 + 75x + 175 = 0 Reorder the terms: 175 + 75x + -20x2 = 0 Solving 175 + 75x + -20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(35 + 15x + -4x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(35 + 15x + -4x2)' equal to zero and attempt to solve: Simplifying 35 + 15x + -4x2 = 0 Solving 35 + 15x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -8.75 + -3.75x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -3.75x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -3.75x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -3.75x + x2 = 0 + 8.75 -3.75x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -3.75x + x2 = 8.75 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 8.75 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 8.75 + 3.515625 Combine like terms: 8.75 + 3.515625 = 12.265625 3.515625 + -3.75x + x2 = 12.265625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 12.265625 Calculate the square root of the right side: 3.502231432 Break this problem into two subproblems by setting (x + -1.875) equal to 3.502231432 and -3.502231432.Subproblem 1
x + -1.875 = 3.502231432 Simplifying x + -1.875 = 3.502231432 Reorder the terms: -1.875 + x = 3.502231432 Solving -1.875 + x = 3.502231432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 3.502231432 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 3.502231432 + 1.875 x = 3.502231432 + 1.875 Combine like terms: 3.502231432 + 1.875 = 5.377231432 x = 5.377231432 Simplifying x = 5.377231432Subproblem 2
x + -1.875 = -3.502231432 Simplifying x + -1.875 = -3.502231432 Reorder the terms: -1.875 + x = -3.502231432 Solving -1.875 + x = -3.502231432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -3.502231432 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -3.502231432 + 1.875 x = -3.502231432 + 1.875 Combine like terms: -3.502231432 + 1.875 = -1.627231432 x = -1.627231432 Simplifying x = -1.627231432Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.377231432, -1.627231432}Solution
x = {5.377231432, -1.627231432}
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