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Simplifying 3p2 + -5p + -3 = 0 Reorder the terms: -3 + -5p + 3p2 = 0 Solving -3 + -5p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1 + -1.666666667p + p2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.666666667p + 1 + p2 = 0 + 1 Reorder the terms: -1 + 1 + -1.666666667p + p2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.666666667p + p2 = 0 + 1 -1.666666667p + p2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.666666667p + p2 = 1 The p term is -1.666666667p. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667p + 0.6944444447 + p2 = 1 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667p + p2 = 1 + 0.6944444447 Combine like terms: 1 + 0.6944444447 = 1.6944444447 0.6944444447 + -1.666666667p + p2 = 1.6944444447 Factor a perfect square on the left side: (p + -0.8333333335)(p + -0.8333333335) = 1.6944444447 Calculate the square root of the right side: 1.301708279 Break this problem into two subproblems by setting (p + -0.8333333335) equal to 1.301708279 and -1.301708279.Subproblem 1
p + -0.8333333335 = 1.301708279 Simplifying p + -0.8333333335 = 1.301708279 Reorder the terms: -0.8333333335 + p = 1.301708279 Solving -0.8333333335 + p = 1.301708279 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + p = 1.301708279 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + p = 1.301708279 + 0.8333333335 p = 1.301708279 + 0.8333333335 Combine like terms: 1.301708279 + 0.8333333335 = 2.1350416125 p = 2.1350416125 Simplifying p = 2.1350416125Subproblem 2
p + -0.8333333335 = -1.301708279 Simplifying p + -0.8333333335 = -1.301708279 Reorder the terms: -0.8333333335 + p = -1.301708279 Solving -0.8333333335 + p = -1.301708279 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + p = -1.301708279 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + p = -1.301708279 + 0.8333333335 p = -1.301708279 + 0.8333333335 Combine like terms: -1.301708279 + 0.8333333335 = -0.4683749455 p = -0.4683749455 Simplifying p = -0.4683749455Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.1350416125, -0.4683749455}
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