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Simplifying -1x2 + 14x + 35 = 0 Reorder the terms: 35 + 14x + -1x2 = 0 Solving 35 + 14x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + -14x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -14x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -14x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -14x + x2 = 0 + 35 -14x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -14x + x2 = 35 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 35 + 49 Reorder the terms: 49 + -14x + x2 = 35 + 49 Combine like terms: 35 + 49 = 84 49 + -14x + x2 = 84 Factor a perfect square on the left side: (x + -7)(x + -7) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + -7) equal to 9.16515139 and -9.16515139.Subproblem 1
x + -7 = 9.16515139 Simplifying x + -7 = 9.16515139 Reorder the terms: -7 + x = 9.16515139 Solving -7 + x = 9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 9.16515139 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9.16515139 + 7 x = 9.16515139 + 7 Combine like terms: 9.16515139 + 7 = 16.16515139 x = 16.16515139 Simplifying x = 16.16515139Subproblem 2
x + -7 = -9.16515139 Simplifying x + -7 = -9.16515139 Reorder the terms: -7 + x = -9.16515139 Solving -7 + x = -9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -9.16515139 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9.16515139 + 7 x = -9.16515139 + 7 Combine like terms: -9.16515139 + 7 = -2.16515139 x = -2.16515139 Simplifying x = -2.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.16515139, -2.16515139}
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