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Simplifying 42 + -12p + 0.6p2 = 0 Solving 42 + -12p + 0.6p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. 70 + -20p + p2 = 0 Move the constant term to the right: Add '-70' to each side of the equation. 70 + -20p + -70 + p2 = 0 + -70 Reorder the terms: 70 + -70 + -20p + p2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -20p + p2 = 0 + -70 -20p + p2 = 0 + -70 Combine like terms: 0 + -70 = -70 -20p + p2 = -70 The p term is -20p. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20p + 100 + p2 = -70 + 100 Reorder the terms: 100 + -20p + p2 = -70 + 100 Combine like terms: -70 + 100 = 30 100 + -20p + p2 = 30 Factor a perfect square on the left side: (p + -10)(p + -10) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (p + -10) equal to 5.477225575 and -5.477225575.Subproblem 1
p + -10 = 5.477225575 Simplifying p + -10 = 5.477225575 Reorder the terms: -10 + p = 5.477225575 Solving -10 + p = 5.477225575 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + p = 5.477225575 + 10 Combine like terms: -10 + 10 = 0 0 + p = 5.477225575 + 10 p = 5.477225575 + 10 Combine like terms: 5.477225575 + 10 = 15.477225575 p = 15.477225575 Simplifying p = 15.477225575Subproblem 2
p + -10 = -5.477225575 Simplifying p + -10 = -5.477225575 Reorder the terms: -10 + p = -5.477225575 Solving -10 + p = -5.477225575 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + p = -5.477225575 + 10 Combine like terms: -10 + 10 = 0 0 + p = -5.477225575 + 10 p = -5.477225575 + 10 Combine like terms: -5.477225575 + 10 = 4.522774425 p = 4.522774425 Simplifying p = 4.522774425Solution
The solution to the problem is based on the solutions from the subproblems. p = {15.477225575, 4.522774425}
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