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Simplifying 2x2 + 15x = 24 Reorder the terms: 15x + 2x2 = 24 Solving 15x + 2x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 15x + 2x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12 + 7.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 7.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 7.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 7.5x + x2 = 0 + 12 7.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 7.5x + x2 = 12 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 = 12 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 12 + 14.0625 Combine like terms: 12 + 14.0625 = 26.0625 14.0625 + 7.5x + x2 = 26.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 26.0625 Calculate the square root of the right side: 5.105144464 Break this problem into two subproblems by setting (x + 3.75) equal to 5.105144464 and -5.105144464.Subproblem 1
x + 3.75 = 5.105144464 Simplifying x + 3.75 = 5.105144464 Reorder the terms: 3.75 + x = 5.105144464 Solving 3.75 + x = 5.105144464 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 = 5.105144464 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 5.105144464 + -3.75 x = 5.105144464 + -3.75 Combine like terms: 5.105144464 + -3.75 = 1.355144464 x = 1.355144464 Simplifying x = 1.355144464Subproblem 2
x + 3.75 = -5.105144464 Simplifying x + 3.75 = -5.105144464 Reorder the terms: 3.75 + x = -5.105144464 Solving 3.75 + x = -5.105144464 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 = -5.105144464 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -5.105144464 + -3.75 x = -5.105144464 + -3.75 Combine like terms: -5.105144464 + -3.75 = -8.855144464 x = -8.855144464 Simplifying x = -8.855144464Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.355144464, -8.855144464}
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