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Simplifying 2x2 + 14x + -235 = 0 Reorder the terms: -235 + 14x + 2x2 = 0 Solving -235 + 14x + 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'. -117.5 + 7x + x2 = 0 Move the constant term to the right: Add '117.5' to each side of the equation. -117.5 + 7x + 117.5 + x2 = 0 + 117.5 Reorder the terms: -117.5 + 117.5 + 7x + x2 = 0 + 117.5 Combine like terms: -117.5 + 117.5 = 0.0 0.0 + 7x + x2 = 0 + 117.5 7x + x2 = 0 + 117.5 Combine like terms: 0 + 117.5 = 117.5 7x + x2 = 117.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 117.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 117.5 + 12.25 Combine like terms: 117.5 + 12.25 = 129.75 12.25 + 7x + x2 = 129.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 129.75 Calculate the square root of the right side: 11.39078575 Break this problem into two subproblems by setting (x + 3.5) equal to 11.39078575 and -11.39078575.Subproblem 1
x + 3.5 = 11.39078575 Simplifying x + 3.5 = 11.39078575 Reorder the terms: 3.5 + x = 11.39078575 Solving 3.5 + x = 11.39078575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 11.39078575 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 11.39078575 + -3.5 x = 11.39078575 + -3.5 Combine like terms: 11.39078575 + -3.5 = 7.89078575 x = 7.89078575 Simplifying x = 7.89078575Subproblem 2
x + 3.5 = -11.39078575 Simplifying x + 3.5 = -11.39078575 Reorder the terms: 3.5 + x = -11.39078575 Solving 3.5 + x = -11.39078575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -11.39078575 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -11.39078575 + -3.5 x = -11.39078575 + -3.5 Combine like terms: -11.39078575 + -3.5 = -14.89078575 x = -14.89078575 Simplifying x = -14.89078575Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.89078575, -14.89078575}
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