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Simplifying 12p2 + -2p + -13 = 0 Reorder the terms: -13 + -2p + 12p2 = 0 Solving -13 + -2p + 12p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.083333333 + -0.1666666667p + p2 = 0 Move the constant term to the right: Add '1.083333333' to each side of the equation. -1.083333333 + -0.1666666667p + 1.083333333 + p2 = 0 + 1.083333333 Reorder the terms: -1.083333333 + 1.083333333 + -0.1666666667p + p2 = 0 + 1.083333333 Combine like terms: -1.083333333 + 1.083333333 = 0.000000000 0.000000000 + -0.1666666667p + p2 = 0 + 1.083333333 -0.1666666667p + p2 = 0 + 1.083333333 Combine like terms: 0 + 1.083333333 = 1.083333333 -0.1666666667p + p2 = 1.083333333 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 = 1.083333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667p + p2 = 1.083333333 + 0.006944444447 Combine like terms: 1.083333333 + 0.006944444447 = 1.090277777447 0.006944444447 + -0.1666666667p + p2 = 1.090277777447 Factor a perfect square on the left side: (p + -0.08333333335)(p + -0.08333333335) = 1.090277777447 Calculate the square root of the right side: 1.044163674 Break this problem into two subproblems by setting (p + -0.08333333335) equal to 1.044163674 and -1.044163674.Subproblem 1
p + -0.08333333335 = 1.044163674 Simplifying p + -0.08333333335 = 1.044163674 Reorder the terms: -0.08333333335 + p = 1.044163674 Solving -0.08333333335 + p = 1.044163674 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 = 1.044163674 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + p = 1.044163674 + 0.08333333335 p = 1.044163674 + 0.08333333335 Combine like terms: 1.044163674 + 0.08333333335 = 1.12749700735 p = 1.12749700735 Simplifying p = 1.12749700735Subproblem 2
p + -0.08333333335 = -1.044163674 Simplifying p + -0.08333333335 = -1.044163674 Reorder the terms: -0.08333333335 + p = -1.044163674 Solving -0.08333333335 + p = -1.044163674 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 = -1.044163674 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + p = -1.044163674 + 0.08333333335 p = -1.044163674 + 0.08333333335 Combine like terms: -1.044163674 + 0.08333333335 = -0.96083034065 p = -0.96083034065 Simplifying p = -0.96083034065Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.12749700735, -0.96083034065}
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