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Simplifying (8x2 + 3x + -2) + (2x2 + 7x + -2) = 0 Reorder the terms: (-2 + 3x + 8x2) + (2x2 + 7x + -2) = 0 Remove parenthesis around (-2 + 3x + 8x2) -2 + 3x + 8x2 + (2x2 + 7x + -2) = 0 Reorder the terms: -2 + 3x + 8x2 + (-2 + 7x + 2x2) = 0 Remove parenthesis around (-2 + 7x + 2x2) -2 + 3x + 8x2 + -2 + 7x + 2x2 = 0 Reorder the terms: -2 + -2 + 3x + 7x + 8x2 + 2x2 = 0 Combine like terms: -2 + -2 = -4 -4 + 3x + 7x + 8x2 + 2x2 = 0 Combine like terms: 3x + 7x = 10x -4 + 10x + 8x2 + 2x2 = 0 Combine like terms: 8x2 + 2x2 = 10x2 -4 + 10x + 10x2 = 0 Solving -4 + 10x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 5x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 5x + 5x2)' equal to zero and attempt to solve: Simplifying -2 + 5x + 5x2 = 0 Solving -2 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x + x2 = 0 + 0.4 x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 x + x2 = 0.4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.4 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.4 + 0.25 Combine like terms: 0.4 + 0.25 = 0.65 1.25 + x2 = 0.65 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.65 Calculate the square root of the right side: 0.806225775 Break this problem into two subproblems by setting (x + 0.5) equal to 0.806225775 and -0.806225775.Subproblem 1
x + 0.5 = 0.806225775 Simplifying x + 0.5 = 0.806225775 Reorder the terms: 0.5 + x = 0.806225775 Solving 0.5 + x = 0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.806225775 + -0.5 x = 0.806225775 + -0.5 Combine like terms: 0.806225775 + -0.5 = 0.306225775 x = 0.306225775 Simplifying x = 0.306225775Subproblem 2
x + 0.5 = -0.806225775 Simplifying x + 0.5 = -0.806225775 Reorder the terms: 0.5 + x = -0.806225775 Solving 0.5 + x = -0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.806225775 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.806225775 + -0.5 x = -0.806225775 + -0.5 Combine like terms: -0.806225775 + -0.5 = -1.306225775 x = -1.306225775 Simplifying x = -1.306225775Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.306225775, -1.306225775}Solution
x = {0.306225775, -1.306225775}
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