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Simplifying 2x2 + 14x = -9 Reorder the terms: 14x + 2x2 = -9 Solving 14x + 2x2 = -9 Solving for variable 'x'. Reorder the terms: 9 + 14x + 2x2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + 14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 7x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 7x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 7x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 7x + x2 = 0 + -4.5 7x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 7x + x2 = -4.5 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 = -4.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -4.5 + 12.25 Combine like terms: -4.5 + 12.25 = 7.75 12.25 + 7x + x2 = 7.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (x + 3.5) equal to 2.783882181 and -2.783882181.Subproblem 1
x + 3.5 = 2.783882181 Simplifying x + 3.5 = 2.783882181 Reorder the terms: 3.5 + x = 2.783882181 Solving 3.5 + x = 2.783882181 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 = 2.783882181 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.783882181 + -3.5 x = 2.783882181 + -3.5 Combine like terms: 2.783882181 + -3.5 = -0.716117819 x = -0.716117819 Simplifying x = -0.716117819Subproblem 2
x + 3.5 = -2.783882181 Simplifying x + 3.5 = -2.783882181 Reorder the terms: 3.5 + x = -2.783882181 Solving 3.5 + x = -2.783882181 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 = -2.783882181 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.783882181 + -3.5 x = -2.783882181 + -3.5 Combine like terms: -2.783882181 + -3.5 = -6.283882181 x = -6.283882181 Simplifying x = -6.283882181Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.716117819, -6.283882181}
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