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Simplifying 2x2 + -45x + 20 = 0 Reorder the terms: 20 + -45x + 2x2 = 0 Solving 20 + -45x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10 + -22.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -22.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -22.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -22.5x + x2 = 0 + -10 -22.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -22.5x + x2 = -10 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 = -10 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = -10 + 126.5625 Combine like terms: -10 + 126.5625 = 116.5625 126.5625 + -22.5x + x2 = 116.5625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 116.5625 Calculate the square root of the right side: 10.796411441 Break this problem into two subproblems by setting (x + -11.25) equal to 10.796411441 and -10.796411441.Subproblem 1
x + -11.25 = 10.796411441 Simplifying x + -11.25 = 10.796411441 Reorder the terms: -11.25 + x = 10.796411441 Solving -11.25 + x = 10.796411441 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 = 10.796411441 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 10.796411441 + 11.25 x = 10.796411441 + 11.25 Combine like terms: 10.796411441 + 11.25 = 22.046411441 x = 22.046411441 Simplifying x = 22.046411441Subproblem 2
x + -11.25 = -10.796411441 Simplifying x + -11.25 = -10.796411441 Reorder the terms: -11.25 + x = -10.796411441 Solving -11.25 + x = -10.796411441 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 = -10.796411441 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -10.796411441 + 11.25 x = -10.796411441 + 11.25 Combine like terms: -10.796411441 + 11.25 = 0.453588559 x = 0.453588559 Simplifying x = 0.453588559Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.046411441, 0.453588559}
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