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Simplifying (2x + -9) * x = 90 Reorder the terms: (-9 + 2x) * x = 90 Reorder the terms for easier multiplication: x(-9 + 2x) = 90 (-9 * x + 2x * x) = 90 (-9x + 2x2) = 90 Solving -9x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -9x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -45 + -4.5x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -4.5x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -4.5x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -4.5x + x2 = 0 + 45 -4.5x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -4.5x + x2 = 45 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 = 45 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 45 + 5.0625 Combine like terms: 45 + 5.0625 = 50.0625 5.0625 + -4.5x + x2 = 50.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 50.0625 Calculate the square root of the right side: 7.075485849 Break this problem into two subproblems by setting (x + -2.25) equal to 7.075485849 and -7.075485849.Subproblem 1
x + -2.25 = 7.075485849 Simplifying x + -2.25 = 7.075485849 Reorder the terms: -2.25 + x = 7.075485849 Solving -2.25 + x = 7.075485849 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 = 7.075485849 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 7.075485849 + 2.25 x = 7.075485849 + 2.25 Combine like terms: 7.075485849 + 2.25 = 9.325485849 x = 9.325485849 Simplifying x = 9.325485849Subproblem 2
x + -2.25 = -7.075485849 Simplifying x + -2.25 = -7.075485849 Reorder the terms: -2.25 + x = -7.075485849 Solving -2.25 + x = -7.075485849 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 = -7.075485849 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -7.075485849 + 2.25 x = -7.075485849 + 2.25 Combine like terms: -7.075485849 + 2.25 = -4.825485849 x = -4.825485849 Simplifying x = -4.825485849Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.325485849, -4.825485849}
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