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Simplifying 4x2 + 15x + -105 = 0 Reorder the terms: -105 + 15x + 4x2 = 0 Solving -105 + 15x + 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'. -26.25 + 3.75x + x2 = 0 Move the constant term to the right: Add '26.25' to each side of the equation. -26.25 + 3.75x + 26.25 + x2 = 0 + 26.25 Reorder the terms: -26.25 + 26.25 + 3.75x + x2 = 0 + 26.25 Combine like terms: -26.25 + 26.25 = 0.00 0.00 + 3.75x + x2 = 0 + 26.25 3.75x + x2 = 0 + 26.25 Combine like terms: 0 + 26.25 = 26.25 3.75x + x2 = 26.25 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 26.25 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 26.25 + 3.515625 Combine like terms: 26.25 + 3.515625 = 29.765625 3.515625 + 3.75x + x2 = 29.765625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 29.765625 Calculate the square root of the right side: 5.455788211 Break this problem into two subproblems by setting (x + 1.875) equal to 5.455788211 and -5.455788211.Subproblem 1
x + 1.875 = 5.455788211 Simplifying x + 1.875 = 5.455788211 Reorder the terms: 1.875 + x = 5.455788211 Solving 1.875 + x = 5.455788211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 5.455788211 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 5.455788211 + -1.875 x = 5.455788211 + -1.875 Combine like terms: 5.455788211 + -1.875 = 3.580788211 x = 3.580788211 Simplifying x = 3.580788211Subproblem 2
x + 1.875 = -5.455788211 Simplifying x + 1.875 = -5.455788211 Reorder the terms: 1.875 + x = -5.455788211 Solving 1.875 + x = -5.455788211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -5.455788211 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -5.455788211 + -1.875 x = -5.455788211 + -1.875 Combine like terms: -5.455788211 + -1.875 = -7.330788211 x = -7.330788211 Simplifying x = -7.330788211Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.580788211, -7.330788211}
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