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Simplifying 4x2 + -61x + -225 = 0 Reorder the terms: -225 + -61x + 4x2 = 0 Solving -225 + -61x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -56.25 + -15.25x + x2 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + -15.25x + 56.25 + x2 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + -15.25x + x2 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + -15.25x + x2 = 0 + 56.25 -15.25x + x2 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 -15.25x + x2 = 56.25 The x term is -15.25x. Take half its coefficient (-7.625). Square it (58.140625) and add it to both sides. Add '58.140625' to each side of the equation. -15.25x + 58.140625 + x2 = 56.25 + 58.140625 Reorder the terms: 58.140625 + -15.25x + x2 = 56.25 + 58.140625 Combine like terms: 56.25 + 58.140625 = 114.390625 58.140625 + -15.25x + x2 = 114.390625 Factor a perfect square on the left side: (x + -7.625)(x + -7.625) = 114.390625 Calculate the square root of the right side: 10.6953553 Break this problem into two subproblems by setting (x + -7.625) equal to 10.6953553 and -10.6953553.Subproblem 1
x + -7.625 = 10.6953553 Simplifying x + -7.625 = 10.6953553 Reorder the terms: -7.625 + x = 10.6953553 Solving -7.625 + x = 10.6953553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.625' to each side of the equation. -7.625 + 7.625 + x = 10.6953553 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + x = 10.6953553 + 7.625 x = 10.6953553 + 7.625 Combine like terms: 10.6953553 + 7.625 = 18.3203553 x = 18.3203553 Simplifying x = 18.3203553Subproblem 2
x + -7.625 = -10.6953553 Simplifying x + -7.625 = -10.6953553 Reorder the terms: -7.625 + x = -10.6953553 Solving -7.625 + x = -10.6953553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.625' to each side of the equation. -7.625 + 7.625 + x = -10.6953553 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + x = -10.6953553 + 7.625 x = -10.6953553 + 7.625 Combine like terms: -10.6953553 + 7.625 = -3.0703553 x = -3.0703553 Simplifying x = -3.0703553Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.3203553, -3.0703553}
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