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Simplifying 25x2 + -7x + -125 = 0 Reorder the terms: -125 + -7x + 25x2 = 0 Solving -125 + -7x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -5 + -0.28x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.28x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.28x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.28x + x2 = 0 + 5 -0.28x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.28x + x2 = 5 The x term is -0.28x. Take half its coefficient (-0.14). Square it (0.0196) and add it to both sides. Add '0.0196' to each side of the equation. -0.28x + 0.0196 + x2 = 5 + 0.0196 Reorder the terms: 0.0196 + -0.28x + x2 = 5 + 0.0196 Combine like terms: 5 + 0.0196 = 5.0196 0.0196 + -0.28x + x2 = 5.0196 Factor a perfect square on the left side: (x + -0.14)(x + -0.14) = 5.0196 Calculate the square root of the right side: 2.240446384 Break this problem into two subproblems by setting (x + -0.14) equal to 2.240446384 and -2.240446384.Subproblem 1
x + -0.14 = 2.240446384 Simplifying x + -0.14 = 2.240446384 Reorder the terms: -0.14 + x = 2.240446384 Solving -0.14 + x = 2.240446384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.14' to each side of the equation. -0.14 + 0.14 + x = 2.240446384 + 0.14 Combine like terms: -0.14 + 0.14 = 0.00 0.00 + x = 2.240446384 + 0.14 x = 2.240446384 + 0.14 Combine like terms: 2.240446384 + 0.14 = 2.380446384 x = 2.380446384 Simplifying x = 2.380446384Subproblem 2
x + -0.14 = -2.240446384 Simplifying x + -0.14 = -2.240446384 Reorder the terms: -0.14 + x = -2.240446384 Solving -0.14 + x = -2.240446384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.14' to each side of the equation. -0.14 + 0.14 + x = -2.240446384 + 0.14 Combine like terms: -0.14 + 0.14 = 0.00 0.00 + x = -2.240446384 + 0.14 x = -2.240446384 + 0.14 Combine like terms: -2.240446384 + 0.14 = -2.100446384 x = -2.100446384 Simplifying x = -2.100446384Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.380446384, -2.100446384}
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