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Simplifying (2x2) + 15x + -12 = 1 Reorder the terms: -12 + 15x + (2x2) = 1 Solving -12 + 15x + (2x2) = 1 Solving for variable 'x'. Reorder the terms: -12 + -1 + 15x + (2x2) = 1 + -1 Combine like terms: -12 + -1 = -13 -13 + 15x + (2x2) = 1 + -1 Combine like terms: 1 + -1 = 0 -13 + 15x + (2x2) = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 7.5x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 7.5x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 7.5x + x2 = 0 + 6.5 7.5x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 7.5x + x2 = 6.5 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 = 6.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 6.5 + 14.0625 Combine like terms: 6.5 + 14.0625 = 20.5625 14.0625 + 7.5x + x2 = 20.5625 Factor a perfect square on the left side: ((x) + 3.75)((x) + 3.75) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting ((x) + 3.75) equal to 4.534589287 and -4.534589287.Subproblem 1
(x) + 3.75 = 4.534589287 Simplifying (x) + 3.75 = 4.534589287 x + 3.75 = 4.534589287 Reorder the terms: 3.75 + x = 4.534589287 Solving 3.75 + x = 4.534589287 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 = 4.534589287 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.534589287 + -3.75 x = 4.534589287 + -3.75 Combine like terms: 4.534589287 + -3.75 = 0.784589287 x = 0.784589287 Simplifying x = 0.784589287Subproblem 2
(x) + 3.75 = -4.534589287 Simplifying (x) + 3.75 = -4.534589287 x + 3.75 = -4.534589287 Reorder the terms: 3.75 + x = -4.534589287 Solving 3.75 + x = -4.534589287 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 = -4.534589287 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.534589287 + -3.75 x = -4.534589287 + -3.75 Combine like terms: -4.534589287 + -3.75 = -8.284589287 x = -8.284589287 Simplifying x = -8.284589287Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.784589287, -8.284589287}
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