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Simplifying 24x + 15 = 2x(3 + 4x) Reorder the terms: 15 + 24x = 2x(3 + 4x) 15 + 24x = (3 * 2x + 4x * 2x) 15 + 24x = (6x + 8x2) Solving 15 + 24x = 6x + 8x2 Solving for variable 'x'. Combine like terms: 24x + -6x = 18x 15 + 18x + -8x2 = 6x + 8x2 + -6x + -8x2 Reorder the terms: 15 + 18x + -8x2 = 6x + -6x + 8x2 + -8x2 Combine like terms: 6x + -6x = 0 15 + 18x + -8x2 = 0 + 8x2 + -8x2 15 + 18x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 15 + 18x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.875 + -2.25x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -2.25x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -2.25x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -2.25x + x2 = 0 + 1.875 -2.25x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -2.25x + x2 = 1.875 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 1.875 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 1.875 + 1.265625 Combine like terms: 1.875 + 1.265625 = 3.140625 1.265625 + -2.25x + x2 = 3.140625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + -1.125) equal to 1.77218086 and -1.77218086.Subproblem 1
x + -1.125 = 1.77218086 Simplifying x + -1.125 = 1.77218086 Reorder the terms: -1.125 + x = 1.77218086 Solving -1.125 + x = 1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.77218086 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.77218086 + 1.125 x = 1.77218086 + 1.125 Combine like terms: 1.77218086 + 1.125 = 2.89718086 x = 2.89718086 Simplifying x = 2.89718086Subproblem 2
x + -1.125 = -1.77218086 Simplifying x + -1.125 = -1.77218086 Reorder the terms: -1.125 + x = -1.77218086 Solving -1.125 + x = -1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.77218086 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.77218086 + 1.125 x = -1.77218086 + 1.125 Combine like terms: -1.77218086 + 1.125 = -0.64718086 x = -0.64718086 Simplifying x = -0.64718086Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.89718086, -0.64718086}
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