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Simplifying 5p2 + -30p = 29 Reorder the terms: -30p + 5p2 = 29 Solving -30p + 5p2 = 29 Solving for variable 'p'. Reorder the terms: -29 + -30p + 5p2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + -30p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.8 + -6p + p2 = 0 Move the constant term to the right: Add '5.8' to each side of the equation. -5.8 + -6p + 5.8 + p2 = 0 + 5.8 Reorder the terms: -5.8 + 5.8 + -6p + p2 = 0 + 5.8 Combine like terms: -5.8 + 5.8 = 0.0 0.0 + -6p + p2 = 0 + 5.8 -6p + p2 = 0 + 5.8 Combine like terms: 0 + 5.8 = 5.8 -6p + p2 = 5.8 The p term is -6p. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6p + 9 + p2 = 5.8 + 9 Reorder the terms: 9 + -6p + p2 = 5.8 + 9 Combine like terms: 5.8 + 9 = 14.8 9 + -6p + p2 = 14.8 Factor a perfect square on the left side: (p + -3)(p + -3) = 14.8 Calculate the square root of the right side: 3.847076812 Break this problem into two subproblems by setting (p + -3) equal to 3.847076812 and -3.847076812.Subproblem 1
p + -3 = 3.847076812 Simplifying p + -3 = 3.847076812 Reorder the terms: -3 + p = 3.847076812 Solving -3 + p = 3.847076812 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = 3.847076812 + 3 Combine like terms: -3 + 3 = 0 0 + p = 3.847076812 + 3 p = 3.847076812 + 3 Combine like terms: 3.847076812 + 3 = 6.847076812 p = 6.847076812 Simplifying p = 6.847076812Subproblem 2
p + -3 = -3.847076812 Simplifying p + -3 = -3.847076812 Reorder the terms: -3 + p = -3.847076812 Solving -3 + p = -3.847076812 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = -3.847076812 + 3 Combine like terms: -3 + 3 = 0 0 + p = -3.847076812 + 3 p = -3.847076812 + 3 Combine like terms: -3.847076812 + 3 = -0.847076812 p = -0.847076812 Simplifying p = -0.847076812Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.847076812, -0.847076812}
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