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Simplifying 5(x + 5)(x + -10) = 8.7 Reorder the terms: 5(5 + x)(x + -10) = 8.7 Reorder the terms: 5(5 + x)(-10 + x) = 8.7 Multiply (5 + x) * (-10 + x) 5(5(-10 + x) + x(-10 + x)) = 8.7 5((-10 * 5 + x * 5) + x(-10 + x)) = 8.7 5((-50 + 5x) + x(-10 + x)) = 8.7 5(-50 + 5x + (-10 * x + x * x)) = 8.7 5(-50 + 5x + (-10x + x2)) = 8.7 Combine like terms: 5x + -10x = -5x 5(-50 + -5x + x2) = 8.7 (-50 * 5 + -5x * 5 + x2 * 5) = 8.7 (-250 + -25x + 5x2) = 8.7 Solving -250 + -25x + 5x2 = 8.7 Solving for variable 'x'. Reorder the terms: -250 + -8.7 + -25x + 5x2 = 8.7 + -8.7 Combine like terms: -250 + -8.7 = -258.7 -258.7 + -25x + 5x2 = 8.7 + -8.7 Combine like terms: 8.7 + -8.7 = 0.0 -258.7 + -25x + 5x2 = 0.0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -51.74 + -5x + x2 = 0.0 Move the constant term to the right: Add '51.74' to each side of the equation. -51.74 + -5x + 51.74 + x2 = 0.0 + 51.74 Reorder the terms: -51.74 + 51.74 + -5x + x2 = 0.0 + 51.74 Combine like terms: -51.74 + 51.74 = 0.00 0.00 + -5x + x2 = 0.0 + 51.74 -5x + x2 = 0.0 + 51.74 Combine like terms: 0.0 + 51.74 = 51.74 -5x + x2 = 51.74 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 51.74 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 51.74 + 6.25 Combine like terms: 51.74 + 6.25 = 57.99 6.25 + -5x + x2 = 57.99 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 57.99 Calculate the square root of the right side: 7.615116545 Break this problem into two subproblems by setting (x + -2.5) equal to 7.615116545 and -7.615116545.Subproblem 1
x + -2.5 = 7.615116545 Simplifying x + -2.5 = 7.615116545 Reorder the terms: -2.5 + x = 7.615116545 Solving -2.5 + x = 7.615116545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 7.615116545 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 7.615116545 + 2.5 x = 7.615116545 + 2.5 Combine like terms: 7.615116545 + 2.5 = 10.115116545 x = 10.115116545 Simplifying x = 10.115116545Subproblem 2
x + -2.5 = -7.615116545 Simplifying x + -2.5 = -7.615116545 Reorder the terms: -2.5 + x = -7.615116545 Solving -2.5 + x = -7.615116545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -7.615116545 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -7.615116545 + 2.5 x = -7.615116545 + 2.5 Combine like terms: -7.615116545 + 2.5 = -5.115116545 x = -5.115116545 Simplifying x = -5.115116545Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.115116545, -5.115116545}
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