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Simplifying 2x2 + 21x + -90 = 0 Reorder the terms: -90 + 21x + 2x2 = 0 Solving -90 + 21x + 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'. -45 + 10.5x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 10.5x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 10.5x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 10.5x + x2 = 0 + 45 10.5x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 10.5x + x2 = 45 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 45 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 45 + 27.5625 Combine like terms: 45 + 27.5625 = 72.5625 27.5625 + 10.5x + x2 = 72.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 72.5625 Calculate the square root of the right side: 8.518362519 Break this problem into two subproblems by setting (x + 5.25) equal to 8.518362519 and -8.518362519.Subproblem 1
x + 5.25 = 8.518362519 Simplifying x + 5.25 = 8.518362519 Reorder the terms: 5.25 + x = 8.518362519 Solving 5.25 + x = 8.518362519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 8.518362519 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 8.518362519 + -5.25 x = 8.518362519 + -5.25 Combine like terms: 8.518362519 + -5.25 = 3.268362519 x = 3.268362519 Simplifying x = 3.268362519Subproblem 2
x + 5.25 = -8.518362519 Simplifying x + 5.25 = -8.518362519 Reorder the terms: 5.25 + x = -8.518362519 Solving 5.25 + x = -8.518362519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -8.518362519 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -8.518362519 + -5.25 x = -8.518362519 + -5.25 Combine like terms: -8.518362519 + -5.25 = -13.768362519 x = -13.768362519 Simplifying x = -13.768362519Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.268362519, -13.768362519}
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