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Simplifying 40x2 + -180x + -902.5 = 0 Reorder the terms: -902.5 + -180x + 40x2 = 0 Solving -902.5 + -180x + 40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -22.5625 + -4.5x + x2 = 0 Move the constant term to the right: Add '22.5625' to each side of the equation. -22.5625 + -4.5x + 22.5625 + x2 = 0 + 22.5625 Reorder the terms: -22.5625 + 22.5625 + -4.5x + x2 = 0 + 22.5625 Combine like terms: -22.5625 + 22.5625 = 0.0000 0.0000 + -4.5x + x2 = 0 + 22.5625 -4.5x + x2 = 0 + 22.5625 Combine like terms: 0 + 22.5625 = 22.5625 -4.5x + x2 = 22.5625 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 22.5625 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 22.5625 + 5.0625 Combine like terms: 22.5625 + 5.0625 = 27.625 5.0625 + -4.5x + x2 = 27.625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 27.625 Calculate the square root of the right side: 5.25594901 Break this problem into two subproblems by setting (x + -2.25) equal to 5.25594901 and -5.25594901.Subproblem 1
x + -2.25 = 5.25594901 Simplifying x + -2.25 = 5.25594901 Reorder the terms: -2.25 + x = 5.25594901 Solving -2.25 + x = 5.25594901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 5.25594901 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 5.25594901 + 2.25 x = 5.25594901 + 2.25 Combine like terms: 5.25594901 + 2.25 = 7.50594901 x = 7.50594901 Simplifying x = 7.50594901Subproblem 2
x + -2.25 = -5.25594901 Simplifying x + -2.25 = -5.25594901 Reorder the terms: -2.25 + x = -5.25594901 Solving -2.25 + x = -5.25594901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -5.25594901 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -5.25594901 + 2.25 x = -5.25594901 + 2.25 Combine like terms: -5.25594901 + 2.25 = -3.00594901 x = -3.00594901 Simplifying x = -3.00594901Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.50594901, -3.00594901}
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