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Simplifying 5(x + 5)(x + -10) = 12.5x + -3.8 Reorder the terms: 5(5 + x)(x + -10) = 12.5x + -3.8 Reorder the terms: 5(5 + x)(-10 + x) = 12.5x + -3.8 Multiply (5 + x) * (-10 + x) 5(5(-10 + x) + x(-10 + x)) = 12.5x + -3.8 5((-10 * 5 + x * 5) + x(-10 + x)) = 12.5x + -3.8 5((-50 + 5x) + x(-10 + x)) = 12.5x + -3.8 5(-50 + 5x + (-10 * x + x * x)) = 12.5x + -3.8 5(-50 + 5x + (-10x + x2)) = 12.5x + -3.8 Combine like terms: 5x + -10x = -5x 5(-50 + -5x + x2) = 12.5x + -3.8 (-50 * 5 + -5x * 5 + x2 * 5) = 12.5x + -3.8 (-250 + -25x + 5x2) = 12.5x + -3.8 Reorder the terms: -250 + -25x + 5x2 = -3.8 + 12.5x Solving -250 + -25x + 5x2 = -3.8 + 12.5x Solving for variable 'x'. Reorder the terms: -250 + 3.8 + -25x + -12.5x + 5x2 = -3.8 + 12.5x + 3.8 + -12.5x Combine like terms: -250 + 3.8 = -246.2 -246.2 + -25x + -12.5x + 5x2 = -3.8 + 12.5x + 3.8 + -12.5x Combine like terms: -25x + -12.5x = -37.5x -246.2 + -37.5x + 5x2 = -3.8 + 12.5x + 3.8 + -12.5x Reorder the terms: -246.2 + -37.5x + 5x2 = -3.8 + 3.8 + 12.5x + -12.5x Combine like terms: -3.8 + 3.8 = 0.0 -246.2 + -37.5x + 5x2 = 0.0 + 12.5x + -12.5x -246.2 + -37.5x + 5x2 = 12.5x + -12.5x Combine like terms: 12.5x + -12.5x = 0.0 -246.2 + -37.5x + 5x2 = 0.0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -49.24 + -7.5x + x2 = 0.0 Move the constant term to the right: Add '49.24' to each side of the equation. -49.24 + -7.5x + 49.24 + x2 = 0.0 + 49.24 Reorder the terms: -49.24 + 49.24 + -7.5x + x2 = 0.0 + 49.24 Combine like terms: -49.24 + 49.24 = 0.00 0.00 + -7.5x + x2 = 0.0 + 49.24 -7.5x + x2 = 0.0 + 49.24 Combine like terms: 0.0 + 49.24 = 49.24 -7.5x + x2 = 49.24 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 = 49.24 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 49.24 + 14.0625 Combine like terms: 49.24 + 14.0625 = 63.3025 14.0625 + -7.5x + x2 = 63.3025 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 63.3025 Calculate the square root of the right side: 7.956286822 Break this problem into two subproblems by setting (x + -3.75) equal to 7.956286822 and -7.956286822.Subproblem 1
x + -3.75 = 7.956286822 Simplifying x + -3.75 = 7.956286822 Reorder the terms: -3.75 + x = 7.956286822 Solving -3.75 + x = 7.956286822 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 = 7.956286822 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 7.956286822 + 3.75 x = 7.956286822 + 3.75 Combine like terms: 7.956286822 + 3.75 = 11.706286822 x = 11.706286822 Simplifying x = 11.706286822Subproblem 2
x + -3.75 = -7.956286822 Simplifying x + -3.75 = -7.956286822 Reorder the terms: -3.75 + x = -7.956286822 Solving -3.75 + x = -7.956286822 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 = -7.956286822 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -7.956286822 + 3.75 x = -7.956286822 + 3.75 Combine like terms: -7.956286822 + 3.75 = -4.206286822 x = -4.206286822 Simplifying x = -4.206286822Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.706286822, -4.206286822}
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