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Simplifying p(5p + -3) + 6(7p + -4) = 0 Reorder the terms: p(-3 + 5p) + 6(7p + -4) = 0 (-3 * p + 5p * p) + 6(7p + -4) = 0 (-3p + 5p2) + 6(7p + -4) = 0 Reorder the terms: -3p + 5p2 + 6(-4 + 7p) = 0 -3p + 5p2 + (-4 * 6 + 7p * 6) = 0 -3p + 5p2 + (-24 + 42p) = 0 Reorder the terms: -24 + -3p + 42p + 5p2 = 0 Combine like terms: -3p + 42p = 39p -24 + 39p + 5p2 = 0 Solving -24 + 39p + 5p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + 7.8p + p2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + 7.8p + 4.8 + p2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + 7.8p + p2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 7.8p + p2 = 0 + 4.8 7.8p + p2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 7.8p + p2 = 4.8 The p term is 7.8p. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8p + 15.21 + p2 = 4.8 + 15.21 Reorder the terms: 15.21 + 7.8p + p2 = 4.8 + 15.21 Combine like terms: 4.8 + 15.21 = 20.01 15.21 + 7.8p + p2 = 20.01 Factor a perfect square on the left side: (p + 3.9)(p + 3.9) = 20.01 Calculate the square root of the right side: 4.473253849 Break this problem into two subproblems by setting (p + 3.9) equal to 4.473253849 and -4.473253849.Subproblem 1
p + 3.9 = 4.473253849 Simplifying p + 3.9 = 4.473253849 Reorder the terms: 3.9 + p = 4.473253849 Solving 3.9 + p = 4.473253849 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + p = 4.473253849 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + p = 4.473253849 + -3.9 p = 4.473253849 + -3.9 Combine like terms: 4.473253849 + -3.9 = 0.573253849 p = 0.573253849 Simplifying p = 0.573253849Subproblem 2
p + 3.9 = -4.473253849 Simplifying p + 3.9 = -4.473253849 Reorder the terms: 3.9 + p = -4.473253849 Solving 3.9 + p = -4.473253849 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + p = -4.473253849 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + p = -4.473253849 + -3.9 p = -4.473253849 + -3.9 Combine like terms: -4.473253849 + -3.9 = -8.373253849 p = -8.373253849 Simplifying p = -8.373253849Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.573253849, -8.373253849}
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