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Simplifying 2x2 + -16x + -35 = 0 Reorder the terms: -35 + -16x + 2x2 = 0 Solving -35 + -16x + 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'. -17.5 + -8x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -8x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -8x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -8x + x2 = 0 + 17.5 -8x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -8x + x2 = 17.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 17.5 + 16 Reorder the terms: 16 + -8x + x2 = 17.5 + 16 Combine like terms: 17.5 + 16 = 33.5 16 + -8x + x2 = 33.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 33.5 Calculate the square root of the right side: 5.787918451 Break this problem into two subproblems by setting (x + -4) equal to 5.787918451 and -5.787918451.Subproblem 1
x + -4 = 5.787918451 Simplifying x + -4 = 5.787918451 Reorder the terms: -4 + x = 5.787918451 Solving -4 + x = 5.787918451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.787918451 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.787918451 + 4 x = 5.787918451 + 4 Combine like terms: 5.787918451 + 4 = 9.787918451 x = 9.787918451 Simplifying x = 9.787918451Subproblem 2
x + -4 = -5.787918451 Simplifying x + -4 = -5.787918451 Reorder the terms: -4 + x = -5.787918451 Solving -4 + x = -5.787918451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.787918451 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.787918451 + 4 x = -5.787918451 + 4 Combine like terms: -5.787918451 + 4 = -1.787918451 x = -1.787918451 Simplifying x = -1.787918451Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.787918451, -1.787918451}
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