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Simplifying 0 = -2x2 + -15x + -14 Reorder the terms: 0 = -14 + -15x + -2x2 Solving 0 = -14 + -15x + -2x2 Solving for variable 'x'. Combine like terms: 0 + 14 = 14 14 + 15x + 2x2 = -14 + -15x + -2x2 + 14 + 15x + 2x2 Reorder the terms: 14 + 15x + 2x2 = -14 + 14 + -15x + 15x + -2x2 + 2x2 Combine like terms: -14 + 14 = 0 14 + 15x + 2x2 = 0 + -15x + 15x + -2x2 + 2x2 14 + 15x + 2x2 = -15x + 15x + -2x2 + 2x2 Combine like terms: -15x + 15x = 0 14 + 15x + 2x2 = 0 + -2x2 + 2x2 14 + 15x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 14 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7 + 7.5x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 7.5x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 7.5x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 7.5x + x2 = 0 + -7 7.5x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 7.5x + x2 = -7 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = -7 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -7 + 14.0625 Combine like terms: -7 + 14.0625 = 7.0625 14.0625 + 7.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + 3.75) equal to 2.657536453 and -2.657536453.Subproblem 1
x + 3.75 = 2.657536453 Simplifying x + 3.75 = 2.657536453 Reorder the terms: 3.75 + x = 2.657536453 Solving 3.75 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 2.657536453 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 2.657536453 + -3.75 x = 2.657536453 + -3.75 Combine like terms: 2.657536453 + -3.75 = -1.092463547 x = -1.092463547 Simplifying x = -1.092463547Subproblem 2
x + 3.75 = -2.657536453 Simplifying x + 3.75 = -2.657536453 Reorder the terms: 3.75 + x = -2.657536453 Solving 3.75 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -2.657536453 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -2.657536453 + -3.75 x = -2.657536453 + -3.75 Combine like terms: -2.657536453 + -3.75 = -6.407536453 x = -6.407536453 Simplifying x = -6.407536453Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.092463547, -6.407536453}
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