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Simplifying 80 = 5x2 + 100x Reorder the terms: 80 = 100x + 5x2 Solving 80 = 100x + 5x2 Solving for variable 'x'. Reorder the terms: 80 + -100x + -5x2 = 100x + -100x + 5x2 + -5x2 Combine like terms: 100x + -100x = 0 80 + -100x + -5x2 = 0 + 5x2 + -5x2 80 + -100x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 80 + -100x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(16 + -20x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(16 + -20x + -1x2)' equal to zero and attempt to solve: Simplifying 16 + -20x + -1x2 = 0 Solving 16 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + 20x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 20x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 20x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 20x + x2 = 0 + 16 20x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 20x + x2 = 16 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 = 16 + 100 Reorder the terms: 100 + 20x + x2 = 16 + 100 Combine like terms: 16 + 100 = 116 100 + 20x + x2 = 116 Factor a perfect square on the left side: (x + 10)(x + 10) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (x + 10) equal to 10.770329614 and -10.770329614.Subproblem 1
x + 10 = 10.770329614 Simplifying x + 10 = 10.770329614 Reorder the terms: 10 + x = 10.770329614 Solving 10 + x = 10.770329614 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 = 10.770329614 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.770329614 + -10 x = 10.770329614 + -10 Combine like terms: 10.770329614 + -10 = 0.770329614 x = 0.770329614 Simplifying x = 0.770329614Subproblem 2
x + 10 = -10.770329614 Simplifying x + 10 = -10.770329614 Reorder the terms: 10 + x = -10.770329614 Solving 10 + x = -10.770329614 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 = -10.770329614 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.770329614 + -10 x = -10.770329614 + -10 Combine like terms: -10.770329614 + -10 = -20.770329614 x = -20.770329614 Simplifying x = -20.770329614Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.770329614, -20.770329614}Solution
x = {0.770329614, -20.770329614}
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