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Simplifying 3p2 + -7p = -3 Reorder the terms: -7p + 3p2 = -3 Solving -7p + 3p2 = -3 Solving for variable 'p'. Reorder the terms: 3 + -7p + 3p2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + -7p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + -2.333333333p + p2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.333333333p + -1 + p2 = 0 + -1 Reorder the terms: 1 + -1 + -2.333333333p + p2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.333333333p + p2 = 0 + -1 -2.333333333p + p2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.333333333p + p2 = -1 The p term is -2.333333333p. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333p + 1.361111112 + p2 = -1 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333p + p2 = -1 + 1.361111112 Combine like terms: -1 + 1.361111112 = 0.361111112 1.361111112 + -2.333333333p + p2 = 0.361111112 Factor a perfect square on the left side: (p + -1.166666667)(p + -1.166666667) = 0.361111112 Calculate the square root of the right side: 0.600925213 Break this problem into two subproblems by setting (p + -1.166666667) equal to 0.600925213 and -0.600925213.Subproblem 1
p + -1.166666667 = 0.600925213 Simplifying p + -1.166666667 = 0.600925213 Reorder the terms: -1.166666667 + p = 0.600925213 Solving -1.166666667 + p = 0.600925213 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + p = 0.600925213 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + p = 0.600925213 + 1.166666667 p = 0.600925213 + 1.166666667 Combine like terms: 0.600925213 + 1.166666667 = 1.76759188 p = 1.76759188 Simplifying p = 1.76759188Subproblem 2
p + -1.166666667 = -0.600925213 Simplifying p + -1.166666667 = -0.600925213 Reorder the terms: -1.166666667 + p = -0.600925213 Solving -1.166666667 + p = -0.600925213 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + p = -0.600925213 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + p = -0.600925213 + 1.166666667 p = -0.600925213 + 1.166666667 Combine like terms: -0.600925213 + 1.166666667 = 0.565741454 p = 0.565741454 Simplifying p = 0.565741454Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.76759188, 0.565741454}
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