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Simplifying 4x2 = -80x + 490 Reorder the terms: 4x2 = 490 + -80x Solving 4x2 = 490 + -80x Solving for variable 'x'. Reorder the terms: -490 + 80x + 4x2 = 490 + -80x + -490 + 80x Reorder the terms: -490 + 80x + 4x2 = 490 + -490 + -80x + 80x Combine like terms: 490 + -490 = 0 -490 + 80x + 4x2 = 0 + -80x + 80x -490 + 80x + 4x2 = -80x + 80x Combine like terms: -80x + 80x = 0 -490 + 80x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-245 + 40x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-245 + 40x + 2x2)' equal to zero and attempt to solve: Simplifying -245 + 40x + 2x2 = 0 Solving -245 + 40x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -122.5 + 20x + x2 = 0 Move the constant term to the right: Add '122.5' to each side of the equation. -122.5 + 20x + 122.5 + x2 = 0 + 122.5 Reorder the terms: -122.5 + 122.5 + 20x + x2 = 0 + 122.5 Combine like terms: -122.5 + 122.5 = 0.0 0.0 + 20x + x2 = 0 + 122.5 20x + x2 = 0 + 122.5 Combine like terms: 0 + 122.5 = 122.5 20x + x2 = 122.5 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 122.5 + 100 Reorder the terms: 100 + 20x + x2 = 122.5 + 100 Combine like terms: 122.5 + 100 = 222.5 100 + 20x + x2 = 222.5 Factor a perfect square on the left side: (x + 10)(x + 10) = 222.5 Calculate the square root of the right side: 14.91643389 Break this problem into two subproblems by setting (x + 10) equal to 14.91643389 and -14.91643389.Subproblem 1
x + 10 = 14.91643389 Simplifying x + 10 = 14.91643389 Reorder the terms: 10 + x = 14.91643389 Solving 10 + x = 14.91643389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 14.91643389 + -10 Combine like terms: 10 + -10 = 0 0 + x = 14.91643389 + -10 x = 14.91643389 + -10 Combine like terms: 14.91643389 + -10 = 4.91643389 x = 4.91643389 Simplifying x = 4.91643389Subproblem 2
x + 10 = -14.91643389 Simplifying x + 10 = -14.91643389 Reorder the terms: 10 + x = -14.91643389 Solving 10 + x = -14.91643389 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -14.91643389 + -10 Combine like terms: 10 + -10 = 0 0 + x = -14.91643389 + -10 x = -14.91643389 + -10 Combine like terms: -14.91643389 + -10 = -24.91643389 x = -24.91643389 Simplifying x = -24.91643389Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.91643389, -24.91643389}Solution
x = {4.91643389, -24.91643389}
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