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Simplifying 14x2 + -10x2 + 63x + -45 = 0 Reorder the terms: -45 + 63x + 14x2 + -10x2 = 0 Combine like terms: 14x2 + -10x2 = 4x2 -45 + 63x + 4x2 = 0 Solving -45 + 63x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + 15.75x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + 15.75x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + 15.75x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + 15.75x + x2 = 0 + 11.25 15.75x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 15.75x + x2 = 11.25 The x term is 15.75x. Take half its coefficient (7.875). Square it (62.015625) and add it to both sides. Add '62.015625' to each side of the equation. 15.75x + 62.015625 + x2 = 11.25 + 62.015625 Reorder the terms: 62.015625 + 15.75x + x2 = 11.25 + 62.015625 Combine like terms: 11.25 + 62.015625 = 73.265625 62.015625 + 15.75x + x2 = 73.265625 Factor a perfect square on the left side: (x + 7.875)(x + 7.875) = 73.265625 Calculate the square root of the right side: 8.559534158 Break this problem into two subproblems by setting (x + 7.875) equal to 8.559534158 and -8.559534158.Subproblem 1
x + 7.875 = 8.559534158 Simplifying x + 7.875 = 8.559534158 Reorder the terms: 7.875 + x = 8.559534158 Solving 7.875 + x = 8.559534158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.875' to each side of the equation. 7.875 + -7.875 + x = 8.559534158 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + x = 8.559534158 + -7.875 x = 8.559534158 + -7.875 Combine like terms: 8.559534158 + -7.875 = 0.684534158 x = 0.684534158 Simplifying x = 0.684534158Subproblem 2
x + 7.875 = -8.559534158 Simplifying x + 7.875 = -8.559534158 Reorder the terms: 7.875 + x = -8.559534158 Solving 7.875 + x = -8.559534158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.875' to each side of the equation. 7.875 + -7.875 + x = -8.559534158 + -7.875 Combine like terms: 7.875 + -7.875 = 0.000 0.000 + x = -8.559534158 + -7.875 x = -8.559534158 + -7.875 Combine like terms: -8.559534158 + -7.875 = -16.434534158 x = -16.434534158 Simplifying x = -16.434534158Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.684534158, -16.434534158}
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