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Simplifying 3x(5 + -2x) + 24 = -1 (5 * 3x + -2x * 3x) + 24 = -1 (15x + -6x2) + 24 = -1 Reorder the terms: 24 + 15x + -6x2 = -1 Solving 24 + 15x + -6x2 = -1 Solving for variable 'x'. Reorder the terms: 24 + 1 + 15x + -6x2 = -1 + 1 Combine like terms: 24 + 1 = 25 25 + 15x + -6x2 = -1 + 1 Combine like terms: -1 + 1 = 0 25 + 15x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -4.166666667 + -2.5x + x2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + -2.5x + 4.166666667 + x2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + -2.5x + x2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + -2.5x + x2 = 0 + 4.166666667 -2.5x + x2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 -2.5x + x2 = 4.166666667 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 4.166666667 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 4.166666667 + 1.5625 Combine like terms: 4.166666667 + 1.5625 = 5.729166667 1.5625 + -2.5x + x2 = 5.729166667 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 5.729166667 Calculate the square root of the right side: 2.393567769 Break this problem into two subproblems by setting (x + -1.25) equal to 2.393567769 and -2.393567769.Subproblem 1
x + -1.25 = 2.393567769 Simplifying x + -1.25 = 2.393567769 Reorder the terms: -1.25 + x = 2.393567769 Solving -1.25 + x = 2.393567769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.393567769 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.393567769 + 1.25 x = 2.393567769 + 1.25 Combine like terms: 2.393567769 + 1.25 = 3.643567769 x = 3.643567769 Simplifying x = 3.643567769Subproblem 2
x + -1.25 = -2.393567769 Simplifying x + -1.25 = -2.393567769 Reorder the terms: -1.25 + x = -2.393567769 Solving -1.25 + x = -2.393567769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.393567769 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.393567769 + 1.25 x = -2.393567769 + 1.25 Combine like terms: -2.393567769 + 1.25 = -1.143567769 x = -1.143567769 Simplifying x = -1.143567769Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.643567769, -1.143567769}
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