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Simplifying 0 = 4x2 + 80x + -180 Reorder the terms: 0 = -180 + 80x + 4x2 Solving 0 = -180 + 80x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 180 = 180 180 + -80x + -4x2 = -180 + 80x + 4x2 + 180 + -80x + -4x2 Reorder the terms: 180 + -80x + -4x2 = -180 + 180 + 80x + -80x + 4x2 + -4x2 Combine like terms: -180 + 180 = 0 180 + -80x + -4x2 = 0 + 80x + -80x + 4x2 + -4x2 180 + -80x + -4x2 = 80x + -80x + 4x2 + -4x2 Combine like terms: 80x + -80x = 0 180 + -80x + -4x2 = 0 + 4x2 + -4x2 180 + -80x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 180 + -80x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(45 + -20x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(45 + -20x + -1x2)' equal to zero and attempt to solve: Simplifying 45 + -20x + -1x2 = 0 Solving 45 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + 20x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 20x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 20x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 20x + x2 = 0 + 45 20x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 20x + x2 = 45 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 = 45 + 100 Reorder the terms: 100 + 20x + x2 = 45 + 100 Combine like terms: 45 + 100 = 145 100 + 20x + x2 = 145 Factor a perfect square on the left side: (x + 10)(x + 10) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + 10) equal to 12.041594579 and -12.041594579.Subproblem 1
x + 10 = 12.041594579 Simplifying x + 10 = 12.041594579 Reorder the terms: 10 + x = 12.041594579 Solving 10 + x = 12.041594579 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 = 12.041594579 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.041594579 + -10 x = 12.041594579 + -10 Combine like terms: 12.041594579 + -10 = 2.041594579 x = 2.041594579 Simplifying x = 2.041594579Subproblem 2
x + 10 = -12.041594579 Simplifying x + 10 = -12.041594579 Reorder the terms: 10 + x = -12.041594579 Solving 10 + x = -12.041594579 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 = -12.041594579 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.041594579 + -10 x = -12.041594579 + -10 Combine like terms: -12.041594579 + -10 = -22.041594579 x = -22.041594579 Simplifying x = -22.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.041594579, -22.041594579}Solution
x = {2.041594579, -22.041594579}
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