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Simplifying 5p2 + 3 = 12p Reorder the terms: 3 + 5p2 = 12p Solving 3 + 5p2 = 12p Solving for variable 'p'. Reorder the terms: 3 + -12p + 5p2 = 12p + -12p Combine like terms: 12p + -12p = 0 3 + -12p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + -2.4p + p2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -2.4p + -0.6 + p2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -2.4p + p2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -2.4p + p2 = 0 + -0.6 -2.4p + p2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -2.4p + p2 = -0.6 The p term is -2.4p. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4p + 1.44 + p2 = -0.6 + 1.44 Reorder the terms: 1.44 + -2.4p + p2 = -0.6 + 1.44 Combine like terms: -0.6 + 1.44 = 0.84 1.44 + -2.4p + p2 = 0.84 Factor a perfect square on the left side: (p + -1.2)(p + -1.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (p + -1.2) equal to 0.916515139 and -0.916515139.Subproblem 1
p + -1.2 = 0.916515139 Simplifying p + -1.2 = 0.916515139 Reorder the terms: -1.2 + p = 0.916515139 Solving -1.2 + p = 0.916515139 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + p = 0.916515139 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + p = 0.916515139 + 1.2 p = 0.916515139 + 1.2 Combine like terms: 0.916515139 + 1.2 = 2.116515139 p = 2.116515139 Simplifying p = 2.116515139Subproblem 2
p + -1.2 = -0.916515139 Simplifying p + -1.2 = -0.916515139 Reorder the terms: -1.2 + p = -0.916515139 Solving -1.2 + p = -0.916515139 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + p = -0.916515139 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + p = -0.916515139 + 1.2 p = -0.916515139 + 1.2 Combine like terms: -0.916515139 + 1.2 = 0.283484861 p = 0.283484861 Simplifying p = 0.283484861Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.116515139, 0.283484861}
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