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Simplifying 2x2 + 6x + 5 = 4x2 + -20x + 25 Reorder the terms: 5 + 6x + 2x2 = 4x2 + -20x + 25 Reorder the terms: 5 + 6x + 2x2 = 25 + -20x + 4x2 Solving 5 + 6x + 2x2 = 25 + -20x + 4x2 Solving for variable 'x'. Reorder the terms: 5 + -25 + 6x + 20x + 2x2 + -4x2 = 25 + -20x + 4x2 + -25 + 20x + -4x2 Combine like terms: 5 + -25 = -20 -20 + 6x + 20x + 2x2 + -4x2 = 25 + -20x + 4x2 + -25 + 20x + -4x2 Combine like terms: 6x + 20x = 26x -20 + 26x + 2x2 + -4x2 = 25 + -20x + 4x2 + -25 + 20x + -4x2 Combine like terms: 2x2 + -4x2 = -2x2 -20 + 26x + -2x2 = 25 + -20x + 4x2 + -25 + 20x + -4x2 Reorder the terms: -20 + 26x + -2x2 = 25 + -25 + -20x + 20x + 4x2 + -4x2 Combine like terms: 25 + -25 = 0 -20 + 26x + -2x2 = 0 + -20x + 20x + 4x2 + -4x2 -20 + 26x + -2x2 = -20x + 20x + 4x2 + -4x2 Combine like terms: -20x + 20x = 0 -20 + 26x + -2x2 = 0 + 4x2 + -4x2 -20 + 26x + -2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -20 + 26x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 13x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 13x + -1x2)' equal to zero and attempt to solve: Simplifying -10 + 13x + -1x2 = 0 Solving -10 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 10 + -13x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -13x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -13x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -13x + x2 = 0 + -10 -13x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -13x + x2 = -10 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -10 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -10 + 42.25 Combine like terms: -10 + 42.25 = 32.25 42.25 + -13x + x2 = 32.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + -6.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + -6.5 = 5.678908346 Simplifying x + -6.5 = 5.678908346 Reorder the terms: -6.5 + x = 5.678908346 Solving -6.5 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 5.678908346 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 5.678908346 + 6.5 x = 5.678908346 + 6.5 Combine like terms: 5.678908346 + 6.5 = 12.178908346 x = 12.178908346 Simplifying x = 12.178908346Subproblem 2
x + -6.5 = -5.678908346 Simplifying x + -6.5 = -5.678908346 Reorder the terms: -6.5 + x = -5.678908346 Solving -6.5 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -5.678908346 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -5.678908346 + 6.5 x = -5.678908346 + 6.5 Combine like terms: -5.678908346 + 6.5 = 0.821091654 x = 0.821091654 Simplifying x = 0.821091654Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.178908346, 0.821091654}Solution
x = {12.178908346, 0.821091654}
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