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Simplifying 4x2 + 20x = 130 Reorder the terms: 20x + 4x2 = 130 Solving 20x + 4x2 = 130 Solving for variable 'x'. Reorder the terms: -130 + 20x + 4x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + 20x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-65 + 10x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-65 + 10x + 2x2)' equal to zero and attempt to solve: Simplifying -65 + 10x + 2x2 = 0 Solving -65 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -32.5 + 5x + x2 = 0 Move the constant term to the right: Add '32.5' to each side of the equation. -32.5 + 5x + 32.5 + x2 = 0 + 32.5 Reorder the terms: -32.5 + 32.5 + 5x + x2 = 0 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + 5x + x2 = 0 + 32.5 5x + x2 = 0 + 32.5 Combine like terms: 0 + 32.5 = 32.5 5x + x2 = 32.5 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 = 32.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 32.5 + 6.25 Combine like terms: 32.5 + 6.25 = 38.75 6.25 + 5x + x2 = 38.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 38.75 Calculate the square root of the right side: 6.224949799 Break this problem into two subproblems by setting (x + 2.5) equal to 6.224949799 and -6.224949799.Subproblem 1
x + 2.5 = 6.224949799 Simplifying x + 2.5 = 6.224949799 Reorder the terms: 2.5 + x = 6.224949799 Solving 2.5 + x = 6.224949799 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 = 6.224949799 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.224949799 + -2.5 x = 6.224949799 + -2.5 Combine like terms: 6.224949799 + -2.5 = 3.724949799 x = 3.724949799 Simplifying x = 3.724949799Subproblem 2
x + 2.5 = -6.224949799 Simplifying x + 2.5 = -6.224949799 Reorder the terms: 2.5 + x = -6.224949799 Solving 2.5 + x = -6.224949799 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 = -6.224949799 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.224949799 + -2.5 x = -6.224949799 + -2.5 Combine like terms: -6.224949799 + -2.5 = -8.724949799 x = -8.724949799 Simplifying x = -8.724949799Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.724949799, -8.724949799}Solution
x = {3.724949799, -8.724949799}
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