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Simplifying 5p2 + 3p + -10 = 0 Reorder the terms: -10 + 3p + 5p2 = 0 Solving -10 + 3p + 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'. -2 + 0.6p + p2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.6p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + 0.6p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.6p + p2 = 0 + 2 0.6p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.6p + p2 = 2 The p term is 0.6p. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6p + 0.09 + p2 = 2 + 0.09 Reorder the terms: 0.09 + 0.6p + p2 = 2 + 0.09 Combine like terms: 2 + 0.09 = 2.09 0.09 + 0.6p + p2 = 2.09 Factor a perfect square on the left side: (p + 0.3)(p + 0.3) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (p + 0.3) equal to 1.445683229 and -1.445683229.Subproblem 1
p + 0.3 = 1.445683229 Simplifying p + 0.3 = 1.445683229 Reorder the terms: 0.3 + p = 1.445683229 Solving 0.3 + p = 1.445683229 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + p = 1.445683229 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + p = 1.445683229 + -0.3 p = 1.445683229 + -0.3 Combine like terms: 1.445683229 + -0.3 = 1.145683229 p = 1.145683229 Simplifying p = 1.145683229Subproblem 2
p + 0.3 = -1.445683229 Simplifying p + 0.3 = -1.445683229 Reorder the terms: 0.3 + p = -1.445683229 Solving 0.3 + p = -1.445683229 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + p = -1.445683229 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + p = -1.445683229 + -0.3 p = -1.445683229 + -0.3 Combine like terms: -1.445683229 + -0.3 = -1.745683229 p = -1.745683229 Simplifying p = -1.745683229Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.145683229, -1.745683229}
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