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Simplifying 2x2 + 15x + -30 = 0 Reorder the terms: -30 + 15x + 2x2 = 0 Solving -30 + 15x + 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 + 7.5x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 7.5x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 7.5x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 7.5x + x2 = 0 + 15 7.5x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 7.5x + x2 = 15 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 15 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 15 + 14.0625 Combine like terms: 15 + 14.0625 = 29.0625 14.0625 + 7.5x + x2 = 29.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 29.0625 Calculate the square root of the right side: 5.390964663 Break this problem into two subproblems by setting (x + 3.75) equal to 5.390964663 and -5.390964663.Subproblem 1
x + 3.75 = 5.390964663 Simplifying x + 3.75 = 5.390964663 Reorder the terms: 3.75 + x = 5.390964663 Solving 3.75 + x = 5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 5.390964663 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 5.390964663 + -3.75 x = 5.390964663 + -3.75 Combine like terms: 5.390964663 + -3.75 = 1.640964663 x = 1.640964663 Simplifying x = 1.640964663Subproblem 2
x + 3.75 = -5.390964663 Simplifying x + 3.75 = -5.390964663 Reorder the terms: 3.75 + x = -5.390964663 Solving 3.75 + x = -5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -5.390964663 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -5.390964663 + -3.75 x = -5.390964663 + -3.75 Combine like terms: -5.390964663 + -3.75 = -9.140964663 x = -9.140964663 Simplifying x = -9.140964663Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.640964663, -9.140964663}
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