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Simplifying 5x(x + 10) = 45 Reorder the terms: 5x(10 + x) = 45 (10 * 5x + x * 5x) = 45 (50x + 5x2) = 45 Solving 50x + 5x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 50x + 5x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 50x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + 10x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + 10x + x2)' equal to zero and attempt to solve: Simplifying -9 + 10x + x2 = 0 Solving -9 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 10x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 10x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 10x + x2 = 0 + 9 10x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 10x + x2 = 9 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 9 + 25 Reorder the terms: 25 + 10x + x2 = 9 + 25 Combine like terms: 9 + 25 = 34 25 + 10x + x2 = 34 Factor a perfect square on the left side: (x + 5)(x + 5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + 5) equal to 5.830951895 and -5.830951895.Subproblem 1
x + 5 = 5.830951895 Simplifying x + 5 = 5.830951895 Reorder the terms: 5 + x = 5.830951895 Solving 5 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.830951895 + -5 x = 5.830951895 + -5 Combine like terms: 5.830951895 + -5 = 0.830951895 x = 0.830951895 Simplifying x = 0.830951895Subproblem 2
x + 5 = -5.830951895 Simplifying x + 5 = -5.830951895 Reorder the terms: 5 + x = -5.830951895 Solving 5 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.830951895 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.830951895 + -5 x = -5.830951895 + -5 Combine like terms: -5.830951895 + -5 = -10.830951895 x = -10.830951895 Simplifying x = -10.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.830951895, -10.830951895}Solution
x = {0.830951895, -10.830951895}
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