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Simplifying -12p2 + 2p + 20 = -3 Reorder the terms: 20 + 2p + -12p2 = -3 Solving 20 + 2p + -12p2 = -3 Solving for variable 'p'. Reorder the terms: 20 + 3 + 2p + -12p2 = -3 + 3 Combine like terms: 20 + 3 = 23 23 + 2p + -12p2 = -3 + 3 Combine like terms: -3 + 3 = 0 23 + 2p + -12p2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.916666667 + -0.1666666667p + p2 = 0 Move the constant term to the right: Add '1.916666667' to each side of the equation. -1.916666667 + -0.1666666667p + 1.916666667 + p2 = 0 + 1.916666667 Reorder the terms: -1.916666667 + 1.916666667 + -0.1666666667p + p2 = 0 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + -0.1666666667p + p2 = 0 + 1.916666667 -0.1666666667p + p2 = 0 + 1.916666667 Combine like terms: 0 + 1.916666667 = 1.916666667 -0.1666666667p + p2 = 1.916666667 The p term is -0.1666666667p. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667p + 0.006944444447 + p2 = 1.916666667 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667p + p2 = 1.916666667 + 0.006944444447 Combine like terms: 1.916666667 + 0.006944444447 = 1.923611111447 0.006944444447 + -0.1666666667p + p2 = 1.923611111447 Factor a perfect square on the left side: (p + -0.08333333335)(p + -0.08333333335) = 1.923611111447 Calculate the square root of the right side: 1.386943082 Break this problem into two subproblems by setting (p + -0.08333333335) equal to 1.386943082 and -1.386943082.Subproblem 1
p + -0.08333333335 = 1.386943082 Simplifying p + -0.08333333335 = 1.386943082 Reorder the terms: -0.08333333335 + p = 1.386943082 Solving -0.08333333335 + p = 1.386943082 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + p = 1.386943082 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + p = 1.386943082 + 0.08333333335 p = 1.386943082 + 0.08333333335 Combine like terms: 1.386943082 + 0.08333333335 = 1.47027641535 p = 1.47027641535 Simplifying p = 1.47027641535Subproblem 2
p + -0.08333333335 = -1.386943082 Simplifying p + -0.08333333335 = -1.386943082 Reorder the terms: -0.08333333335 + p = -1.386943082 Solving -0.08333333335 + p = -1.386943082 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + p = -1.386943082 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + p = -1.386943082 + 0.08333333335 p = -1.386943082 + 0.08333333335 Combine like terms: -1.386943082 + 0.08333333335 = -1.30360974865 p = -1.30360974865 Simplifying p = -1.30360974865Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.47027641535, -1.30360974865}
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