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Simplifying 4x2 + -90x + 189 = 0 Reorder the terms: 189 + -90x + 4x2 = 0 Solving 189 + -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'. 47.25 + -22.5x + x2 = 0 Move the constant term to the right: Add '-47.25' to each side of the equation. 47.25 + -22.5x + -47.25 + x2 = 0 + -47.25 Reorder the terms: 47.25 + -47.25 + -22.5x + x2 = 0 + -47.25 Combine like terms: 47.25 + -47.25 = 0.00 0.00 + -22.5x + x2 = 0 + -47.25 -22.5x + x2 = 0 + -47.25 Combine like terms: 0 + -47.25 = -47.25 -22.5x + x2 = -47.25 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 = -47.25 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = -47.25 + 126.5625 Combine like terms: -47.25 + 126.5625 = 79.3125 126.5625 + -22.5x + x2 = 79.3125 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 79.3125 Calculate the square root of the right side: 8.905756565 Break this problem into two subproblems by setting (x + -11.25) equal to 8.905756565 and -8.905756565.Subproblem 1
x + -11.25 = 8.905756565 Simplifying x + -11.25 = 8.905756565 Reorder the terms: -11.25 + x = 8.905756565 Solving -11.25 + x = 8.905756565 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 = 8.905756565 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 8.905756565 + 11.25 x = 8.905756565 + 11.25 Combine like terms: 8.905756565 + 11.25 = 20.155756565 x = 20.155756565 Simplifying x = 20.155756565Subproblem 2
x + -11.25 = -8.905756565 Simplifying x + -11.25 = -8.905756565 Reorder the terms: -11.25 + x = -8.905756565 Solving -11.25 + x = -8.905756565 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 = -8.905756565 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -8.905756565 + 11.25 x = -8.905756565 + 11.25 Combine like terms: -8.905756565 + 11.25 = 2.344243435 x = 2.344243435 Simplifying x = 2.344243435Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.155756565, 2.344243435}
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