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Simplifying 4p2 + 20p + -15 = 0 Reorder the terms: -15 + 20p + 4p2 = 0 Solving -15 + 20p + 4p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 5p + p2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 5p + 3.75 + p2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 5p + p2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 5p + p2 = 0 + 3.75 5p + p2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 5p + p2 = 3.75 The p term is 5p. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5p + 6.25 + p2 = 3.75 + 6.25 Reorder the terms: 6.25 + 5p + p2 = 3.75 + 6.25 Combine like terms: 3.75 + 6.25 = 10 6.25 + 5p + p2 = 10 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (p + 2.5) equal to 3.16227766 and -3.16227766.Subproblem 1
p + 2.5 = 3.16227766 Simplifying p + 2.5 = 3.16227766 Reorder the terms: 2.5 + p = 3.16227766 Solving 2.5 + p = 3.16227766 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = 3.16227766 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 3.16227766 + -2.5 p = 3.16227766 + -2.5 Combine like terms: 3.16227766 + -2.5 = 0.66227766 p = 0.66227766 Simplifying p = 0.66227766Subproblem 2
p + 2.5 = -3.16227766 Simplifying p + 2.5 = -3.16227766 Reorder the terms: 2.5 + p = -3.16227766 Solving 2.5 + p = -3.16227766 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = -3.16227766 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -3.16227766 + -2.5 p = -3.16227766 + -2.5 Combine like terms: -3.16227766 + -2.5 = -5.66227766 p = -5.66227766 Simplifying p = -5.66227766Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.66227766, -5.66227766}
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