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Simplifying 2x2 + 21x + 30 = 0 Reorder the terms: 30 + 21x + 2x2 = 0 Solving 30 + 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'. 15 + 10.5x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + 10.5x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 10.5x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 10.5x + x2 = 0 + -15 10.5x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 10.5x + x2 = -15 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 = -15 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = -15 + 27.5625 Combine like terms: -15 + 27.5625 = 12.5625 27.5625 + 10.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + 5.25) equal to 3.54436172 and -3.54436172.Subproblem 1
x + 5.25 = 3.54436172 Simplifying x + 5.25 = 3.54436172 Reorder the terms: 5.25 + x = 3.54436172 Solving 5.25 + x = 3.54436172 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 = 3.54436172 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 3.54436172 + -5.25 x = 3.54436172 + -5.25 Combine like terms: 3.54436172 + -5.25 = -1.70563828 x = -1.70563828 Simplifying x = -1.70563828Subproblem 2
x + 5.25 = -3.54436172 Simplifying x + 5.25 = -3.54436172 Reorder the terms: 5.25 + x = -3.54436172 Solving 5.25 + x = -3.54436172 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 = -3.54436172 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -3.54436172 + -5.25 x = -3.54436172 + -5.25 Combine like terms: -3.54436172 + -5.25 = -8.79436172 x = -8.79436172 Simplifying x = -8.79436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.70563828, -8.79436172}
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