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Simplifying 3p(p + 14) = 5 Reorder the terms: 3p(14 + p) = 5 (14 * 3p + p * 3p) = 5 (42p + 3p2) = 5 Solving 42p + 3p2 = 5 Solving for variable 'p'. Reorder the terms: -5 + 42p + 3p2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 42p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + 14p + p2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 14p + 1.666666667 + p2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 14p + p2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 14p + p2 = 0 + 1.666666667 14p + p2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 14p + p2 = 1.666666667 The p term is 14p. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14p + 49 + p2 = 1.666666667 + 49 Reorder the terms: 49 + 14p + p2 = 1.666666667 + 49 Combine like terms: 1.666666667 + 49 = 50.666666667 49 + 14p + p2 = 50.666666667 Factor a perfect square on the left side: (p + 7)(p + 7) = 50.666666667 Calculate the square root of the right side: 7.118052168 Break this problem into two subproblems by setting (p + 7) equal to 7.118052168 and -7.118052168.Subproblem 1
p + 7 = 7.118052168 Simplifying p + 7 = 7.118052168 Reorder the terms: 7 + p = 7.118052168 Solving 7 + p = 7.118052168 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + p = 7.118052168 + -7 Combine like terms: 7 + -7 = 0 0 + p = 7.118052168 + -7 p = 7.118052168 + -7 Combine like terms: 7.118052168 + -7 = 0.118052168 p = 0.118052168 Simplifying p = 0.118052168Subproblem 2
p + 7 = -7.118052168 Simplifying p + 7 = -7.118052168 Reorder the terms: 7 + p = -7.118052168 Solving 7 + p = -7.118052168 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + p = -7.118052168 + -7 Combine like terms: 7 + -7 = 0 0 + p = -7.118052168 + -7 p = -7.118052168 + -7 Combine like terms: -7.118052168 + -7 = -14.118052168 p = -14.118052168 Simplifying p = -14.118052168Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.118052168, -14.118052168}
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