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Simplifying 100x2 + 175x + -250 = 0 Reorder the terms: -250 + 175x + 100x2 = 0 Solving -250 + 175x + 100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '25'. 25(-10 + 7x + 4x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-10 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying -10 + 7x + 4x2 = 0 Solving -10 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + 1.75x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 1.75x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 1.75x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 1.75x + x2 = 0 + 2.5 1.75x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 1.75x + x2 = 2.5 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 = 2.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 2.5 + 0.765625 Combine like terms: 2.5 + 0.765625 = 3.265625 0.765625 + 1.75x + x2 = 3.265625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (x + 0.875) equal to 1.807104037 and -1.807104037.Subproblem 1
x + 0.875 = 1.807104037 Simplifying x + 0.875 = 1.807104037 Reorder the terms: 0.875 + x = 1.807104037 Solving 0.875 + x = 1.807104037 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 = 1.807104037 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.807104037 + -0.875 x = 1.807104037 + -0.875 Combine like terms: 1.807104037 + -0.875 = 0.932104037 x = 0.932104037 Simplifying x = 0.932104037Subproblem 2
x + 0.875 = -1.807104037 Simplifying x + 0.875 = -1.807104037 Reorder the terms: 0.875 + x = -1.807104037 Solving 0.875 + x = -1.807104037 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 = -1.807104037 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.807104037 + -0.875 x = -1.807104037 + -0.875 Combine like terms: -1.807104037 + -0.875 = -2.682104037 x = -2.682104037 Simplifying x = -2.682104037Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.932104037, -2.682104037}Solution
x = {0.932104037, -2.682104037}
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