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Simplifying 2x2 + -14x + -3 = 0 Reorder the terms: -3 + -14x + 2x2 = 0 Solving -3 + -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'. -1.5 + -7x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -7x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -7x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -7x + x2 = 0 + 1.5 -7x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -7x + x2 = 1.5 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 = 1.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 1.5 + 12.25 Combine like terms: 1.5 + 12.25 = 13.75 12.25 + -7x + x2 = 13.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (x + -3.5) equal to 3.708099244 and -3.708099244.Subproblem 1
x + -3.5 = 3.708099244 Simplifying x + -3.5 = 3.708099244 Reorder the terms: -3.5 + x = 3.708099244 Solving -3.5 + x = 3.708099244 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 = 3.708099244 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.708099244 + 3.5 x = 3.708099244 + 3.5 Combine like terms: 3.708099244 + 3.5 = 7.208099244 x = 7.208099244 Simplifying x = 7.208099244Subproblem 2
x + -3.5 = -3.708099244 Simplifying x + -3.5 = -3.708099244 Reorder the terms: -3.5 + x = -3.708099244 Solving -3.5 + x = -3.708099244 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 = -3.708099244 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.708099244 + 3.5 x = -3.708099244 + 3.5 Combine like terms: -3.708099244 + 3.5 = -0.208099244 x = -0.208099244 Simplifying x = -0.208099244Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.208099244, -0.208099244}
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