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Simplifying 2x2 + 14x + 24 = 9 Reorder the terms: 24 + 14x + 2x2 = 9 Solving 24 + 14x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: 24 + -9 + 14x + 2x2 = 9 + -9 Combine like terms: 24 + -9 = 15 15 + 14x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 15 + 14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 7x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 7x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 7x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 7x + x2 = 0 + -7.5 7x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 7x + x2 = -7.5 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 = -7.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -7.5 + 12.25 Combine like terms: -7.5 + 12.25 = 4.75 12.25 + 7x + x2 = 4.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + 3.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x + 3.5 = 2.179449472 Simplifying x + 3.5 = 2.179449472 Reorder the terms: 3.5 + x = 2.179449472 Solving 3.5 + x = 2.179449472 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 = 2.179449472 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.179449472 + -3.5 x = 2.179449472 + -3.5 Combine like terms: 2.179449472 + -3.5 = -1.320550528 x = -1.320550528 Simplifying x = -1.320550528Subproblem 2
x + 3.5 = -2.179449472 Simplifying x + 3.5 = -2.179449472 Reorder the terms: 3.5 + x = -2.179449472 Solving 3.5 + x = -2.179449472 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 = -2.179449472 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.179449472 + -3.5 x = -2.179449472 + -3.5 Combine like terms: -2.179449472 + -3.5 = -5.679449472 x = -5.679449472 Simplifying x = -5.679449472Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.320550528, -5.679449472}
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