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Simplifying 4x2 + -45x + 90 = 0 Reorder the terms: 90 + -45x + 4x2 = 0 Solving 90 + -45x + 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'. 22.5 + -11.25x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + -11.25x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + -11.25x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + -11.25x + x2 = 0 + -22.5 -11.25x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 -11.25x + x2 = -22.5 The x term is -11.25x. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25x + 31.640625 + x2 = -22.5 + 31.640625 Reorder the terms: 31.640625 + -11.25x + x2 = -22.5 + 31.640625 Combine like terms: -22.5 + 31.640625 = 9.140625 31.640625 + -11.25x + x2 = 9.140625 Factor a perfect square on the left side: (x + -5.625)(x + -5.625) = 9.140625 Calculate the square root of the right side: 3.023346656 Break this problem into two subproblems by setting (x + -5.625) equal to 3.023346656 and -3.023346656.Subproblem 1
x + -5.625 = 3.023346656 Simplifying x + -5.625 = 3.023346656 Reorder the terms: -5.625 + x = 3.023346656 Solving -5.625 + x = 3.023346656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = 3.023346656 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = 3.023346656 + 5.625 x = 3.023346656 + 5.625 Combine like terms: 3.023346656 + 5.625 = 8.648346656 x = 8.648346656 Simplifying x = 8.648346656Subproblem 2
x + -5.625 = -3.023346656 Simplifying x + -5.625 = -3.023346656 Reorder the terms: -5.625 + x = -3.023346656 Solving -5.625 + x = -3.023346656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = -3.023346656 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = -3.023346656 + 5.625 x = -3.023346656 + 5.625 Combine like terms: -3.023346656 + 5.625 = 2.601653344 x = 2.601653344 Simplifying x = 2.601653344Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.648346656, 2.601653344}
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