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Simplifying 2x2 + 15x = -10 + 25x Reorder the terms: 15x + 2x2 = -10 + 25x Solving 15x + 2x2 = -10 + 25x Solving for variable 'x'. Reorder the terms: 10 + 15x + -25x + 2x2 = -10 + 25x + 10 + -25x Combine like terms: 15x + -25x = -10x 10 + -10x + 2x2 = -10 + 25x + 10 + -25x Reorder the terms: 10 + -10x + 2x2 = -10 + 10 + 25x + -25x Combine like terms: -10 + 10 = 0 10 + -10x + 2x2 = 0 + 25x + -25x 10 + -10x + 2x2 = 25x + -25x Combine like terms: 25x + -25x = 0 10 + -10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -5x + x2)' equal to zero and attempt to solve: Simplifying 5 + -5x + x2 = 0 Solving 5 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5x + x2 = 0 + -5 -5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5x + x2 = -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 = -5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -5 + 6.25 Combine like terms: -5 + 6.25 = 1.25 6.25 + -5x + x2 = 1.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -2.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -2.5 = 1.118033989 Simplifying x + -2.5 = 1.118033989 Reorder the terms: -2.5 + x = 1.118033989 Solving -2.5 + x = 1.118033989 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 = 1.118033989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.118033989 + 2.5 x = 1.118033989 + 2.5 Combine like terms: 1.118033989 + 2.5 = 3.618033989 x = 3.618033989 Simplifying x = 3.618033989Subproblem 2
x + -2.5 = -1.118033989 Simplifying x + -2.5 = -1.118033989 Reorder the terms: -2.5 + x = -1.118033989 Solving -2.5 + x = -1.118033989 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 = -1.118033989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.118033989 + 2.5 x = -1.118033989 + 2.5 Combine like terms: -1.118033989 + 2.5 = 1.381966011 x = 1.381966011 Simplifying x = 1.381966011Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.618033989, 1.381966011}Solution
x = {3.618033989, 1.381966011}
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