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Simplifying 3800 + -12p = 3000 + 8p2 Solving 3800 + -12p = 3000 + 8p2 Solving for variable 'p'. Reorder the terms: 3800 + -3000 + -12p + -8p2 = 3000 + 8p2 + -3000 + -8p2 Combine like terms: 3800 + -3000 = 800 800 + -12p + -8p2 = 3000 + 8p2 + -3000 + -8p2 Reorder the terms: 800 + -12p + -8p2 = 3000 + -3000 + 8p2 + -8p2 Combine like terms: 3000 + -3000 = 0 800 + -12p + -8p2 = 0 + 8p2 + -8p2 800 + -12p + -8p2 = 8p2 + -8p2 Combine like terms: 8p2 + -8p2 = 0 800 + -12p + -8p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(200 + -3p + -2p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(200 + -3p + -2p2)' equal to zero and attempt to solve: Simplifying 200 + -3p + -2p2 = 0 Solving 200 + -3p + -2p2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -100 + 1.5p + p2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 1.5p + 100 + p2 = 0 + 100 Reorder the terms: -100 + 100 + 1.5p + p2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 1.5p + p2 = 0 + 100 1.5p + p2 = 0 + 100 Combine like terms: 0 + 100 = 100 1.5p + p2 = 100 The p term is 1.5p. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5p + 0.5625 + p2 = 100 + 0.5625 Reorder the terms: 0.5625 + 1.5p + p2 = 100 + 0.5625 Combine like terms: 100 + 0.5625 = 100.5625 0.5625 + 1.5p + p2 = 100.5625 Factor a perfect square on the left side: (p + 0.75)(p + 0.75) = 100.5625 Calculate the square root of the right side: 10.02808556 Break this problem into two subproblems by setting (p + 0.75) equal to 10.02808556 and -10.02808556.Subproblem 1
p + 0.75 = 10.02808556 Simplifying p + 0.75 = 10.02808556 Reorder the terms: 0.75 + p = 10.02808556 Solving 0.75 + p = 10.02808556 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + p = 10.02808556 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + p = 10.02808556 + -0.75 p = 10.02808556 + -0.75 Combine like terms: 10.02808556 + -0.75 = 9.27808556 p = 9.27808556 Simplifying p = 9.27808556Subproblem 2
p + 0.75 = -10.02808556 Simplifying p + 0.75 = -10.02808556 Reorder the terms: 0.75 + p = -10.02808556 Solving 0.75 + p = -10.02808556 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + p = -10.02808556 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + p = -10.02808556 + -0.75 p = -10.02808556 + -0.75 Combine like terms: -10.02808556 + -0.75 = -10.77808556 p = -10.77808556 Simplifying p = -10.77808556Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.27808556, -10.77808556}Solution
p = {9.27808556, -10.77808556}
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