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Simplifying 2x2 + 20x = 156 Reorder the terms: 20x + 2x2 = 156 Solving 20x + 2x2 = 156 Solving for variable 'x'. Reorder the terms: -156 + 20x + 2x2 = 156 + -156 Combine like terms: 156 + -156 = 0 -156 + 20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-78 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-78 + 10x + x2)' equal to zero and attempt to solve: Simplifying -78 + 10x + x2 = 0 Solving -78 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + 10x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + 10x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 10x + x2 = 0 + 78 10x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 10x + x2 = 78 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 = 78 + 25 Reorder the terms: 25 + 10x + x2 = 78 + 25 Combine like terms: 78 + 25 = 103 25 + 10x + x2 = 103 Factor a perfect square on the left side: (x + 5)(x + 5) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (x + 5) equal to 10.148891565 and -10.148891565.Subproblem 1
x + 5 = 10.148891565 Simplifying x + 5 = 10.148891565 Reorder the terms: 5 + x = 10.148891565 Solving 5 + x = 10.148891565 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 = 10.148891565 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.148891565 + -5 x = 10.148891565 + -5 Combine like terms: 10.148891565 + -5 = 5.148891565 x = 5.148891565 Simplifying x = 5.148891565Subproblem 2
x + 5 = -10.148891565 Simplifying x + 5 = -10.148891565 Reorder the terms: 5 + x = -10.148891565 Solving 5 + x = -10.148891565 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 = -10.148891565 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.148891565 + -5 x = -10.148891565 + -5 Combine like terms: -10.148891565 + -5 = -15.148891565 x = -15.148891565 Simplifying x = -15.148891565Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.148891565, -15.148891565}Solution
x = {5.148891565, -15.148891565}
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