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Simplifying 2x2 + -35x + -30 = 0 Reorder the terms: -30 + -35x + 2x2 = 0 Solving -30 + -35x + 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 + -17.5x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -17.5x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -17.5x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -17.5x + x2 = 0 + 15 -17.5x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -17.5x + x2 = 15 The x term is -17.5x. Take half its coefficient (-8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. -17.5x + 76.5625 + x2 = 15 + 76.5625 Reorder the terms: 76.5625 + -17.5x + x2 = 15 + 76.5625 Combine like terms: 15 + 76.5625 = 91.5625 76.5625 + -17.5x + x2 = 91.5625 Factor a perfect square on the left side: (x + -8.75)(x + -8.75) = 91.5625 Calculate the square root of the right side: 9.568829605 Break this problem into two subproblems by setting (x + -8.75) equal to 9.568829605 and -9.568829605.Subproblem 1
x + -8.75 = 9.568829605 Simplifying x + -8.75 = 9.568829605 Reorder the terms: -8.75 + x = 9.568829605 Solving -8.75 + x = 9.568829605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = 9.568829605 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 9.568829605 + 8.75 x = 9.568829605 + 8.75 Combine like terms: 9.568829605 + 8.75 = 18.318829605 x = 18.318829605 Simplifying x = 18.318829605Subproblem 2
x + -8.75 = -9.568829605 Simplifying x + -8.75 = -9.568829605 Reorder the terms: -8.75 + x = -9.568829605 Solving -8.75 + x = -9.568829605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = -9.568829605 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -9.568829605 + 8.75 x = -9.568829605 + 8.75 Combine like terms: -9.568829605 + 8.75 = -0.818829605 x = -0.818829605 Simplifying x = -0.818829605Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.318829605, -0.818829605}
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