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Simplifying 4x2 + -90x + 225 = 0 Reorder the terms: 225 + -90x + 4x2 = 0 Solving 225 + -90x + 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 + -22.5x + x2 = 0 Move the constant term to the right: Add '-56.25' to each side of the equation. 56.25 + -22.5x + -56.25 + x2 = 0 + -56.25 Reorder the terms: 56.25 + -56.25 + -22.5x + x2 = 0 + -56.25 Combine like terms: 56.25 + -56.25 = 0.00 0.00 + -22.5x + x2 = 0 + -56.25 -22.5x + x2 = 0 + -56.25 Combine like terms: 0 + -56.25 = -56.25 -22.5x + x2 = -56.25 The x term is -22.5x. Take half its coefficient (-11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. -22.5x + 126.5625 + x2 = -56.25 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = -56.25 + 126.5625 Combine like terms: -56.25 + 126.5625 = 70.3125 126.5625 + -22.5x + x2 = 70.3125 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 70.3125 Calculate the square root of the right side: 8.385254916 Break this problem into two subproblems by setting (x + -11.25) equal to 8.385254916 and -8.385254916.Subproblem 1
x + -11.25 = 8.385254916 Simplifying x + -11.25 = 8.385254916 Reorder the terms: -11.25 + x = 8.385254916 Solving -11.25 + x = 8.385254916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 8.385254916 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 8.385254916 + 11.25 x = 8.385254916 + 11.25 Combine like terms: 8.385254916 + 11.25 = 19.635254916 x = 19.635254916 Simplifying x = 19.635254916Subproblem 2
x + -11.25 = -8.385254916 Simplifying x + -11.25 = -8.385254916 Reorder the terms: -11.25 + x = -8.385254916 Solving -11.25 + x = -8.385254916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -8.385254916 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -8.385254916 + 11.25 x = -8.385254916 + 11.25 Combine like terms: -8.385254916 + 11.25 = 2.864745084 x = 2.864745084 Simplifying x = 2.864745084Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.635254916, 2.864745084}
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