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Simplifying 24x = (5x + 1)(x + -1) Reorder the terms: 24x = (1 + 5x)(x + -1) Reorder the terms: 24x = (1 + 5x)(-1 + x) Multiply (1 + 5x) * (-1 + x) 24x = (1(-1 + x) + 5x * (-1 + x)) 24x = ((-1 * 1 + x * 1) + 5x * (-1 + x)) 24x = ((-1 + 1x) + 5x * (-1 + x)) 24x = (-1 + 1x + (-1 * 5x + x * 5x)) 24x = (-1 + 1x + (-5x + 5x2)) Combine like terms: 1x + -5x = -4x 24x = (-1 + -4x + 5x2) Solving 24x = -1 + -4x + 5x2 Solving for variable 'x'. Reorder the terms: 1 + 24x + 4x + -5x2 = -1 + -4x + 5x2 + 1 + 4x + -5x2 Combine like terms: 24x + 4x = 28x 1 + 28x + -5x2 = -1 + -4x + 5x2 + 1 + 4x + -5x2 Reorder the terms: 1 + 28x + -5x2 = -1 + 1 + -4x + 4x + 5x2 + -5x2 Combine like terms: -1 + 1 = 0 1 + 28x + -5x2 = 0 + -4x + 4x + 5x2 + -5x2 1 + 28x + -5x2 = -4x + 4x + 5x2 + -5x2 Combine like terms: -4x + 4x = 0 1 + 28x + -5x2 = 0 + 5x2 + -5x2 1 + 28x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 1 + 28x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.2 + -5.6x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -5.6x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -5.6x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -5.6x + x2 = 0 + 0.2 -5.6x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -5.6x + x2 = 0.2 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = 0.2 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = 0.2 + 7.84 Combine like terms: 0.2 + 7.84 = 8.04 7.84 + -5.6x + x2 = 8.04 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 8.04 Calculate the square root of the right side: 2.835489376 Break this problem into two subproblems by setting (x + -2.8) equal to 2.835489376 and -2.835489376.Subproblem 1
x + -2.8 = 2.835489376 Simplifying x + -2.8 = 2.835489376 Reorder the terms: -2.8 + x = 2.835489376 Solving -2.8 + x = 2.835489376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 2.835489376 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 2.835489376 + 2.8 x = 2.835489376 + 2.8 Combine like terms: 2.835489376 + 2.8 = 5.635489376 x = 5.635489376 Simplifying x = 5.635489376Subproblem 2
x + -2.8 = -2.835489376 Simplifying x + -2.8 = -2.835489376 Reorder the terms: -2.8 + x = -2.835489376 Solving -2.8 + x = -2.835489376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -2.835489376 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -2.835489376 + 2.8 x = -2.835489376 + 2.8 Combine like terms: -2.835489376 + 2.8 = -0.035489376 x = -0.035489376 Simplifying x = -0.035489376Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.635489376, -0.035489376}
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