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Simplifying 20x2 + -35x + -100 = 0 Reorder the terms: -100 + -35x + 20x2 = 0 Solving -100 + -35x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + -7x + 4x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-20 + -7x + 4x2)' equal to zero and attempt to solve: Simplifying -20 + -7x + 4x2 = 0 Solving -20 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5 + -1.75x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1.75x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -1.75x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1.75x + x2 = 0 + 5 -1.75x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1.75x + x2 = 5 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 5 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 5 + 0.765625 Combine like terms: 5 + 0.765625 = 5.765625 0.765625 + -1.75x + x2 = 5.765625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 5.765625 Calculate the square root of the right side: 2.401171589 Break this problem into two subproblems by setting (x + -0.875) equal to 2.401171589 and -2.401171589.Subproblem 1
x + -0.875 = 2.401171589 Simplifying x + -0.875 = 2.401171589 Reorder the terms: -0.875 + x = 2.401171589 Solving -0.875 + x = 2.401171589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 2.401171589 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 2.401171589 + 0.875 x = 2.401171589 + 0.875 Combine like terms: 2.401171589 + 0.875 = 3.276171589 x = 3.276171589 Simplifying x = 3.276171589Subproblem 2
x + -0.875 = -2.401171589 Simplifying x + -0.875 = -2.401171589 Reorder the terms: -0.875 + x = -2.401171589 Solving -0.875 + x = -2.401171589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -2.401171589 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -2.401171589 + 0.875 x = -2.401171589 + 0.875 Combine like terms: -2.401171589 + 0.875 = -1.526171589 x = -1.526171589 Simplifying x = -1.526171589Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.276171589, -1.526171589}Solution
x = {3.276171589, -1.526171589}
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