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Simplifying -4p2 + -7p + -11 = -10 Reorder the terms: -11 + -7p + -4p2 = -10 Solving -11 + -7p + -4p2 = -10 Solving for variable 'p'. Reorder the terms: -11 + 10 + -7p + -4p2 = -10 + 10 Combine like terms: -11 + 10 = -1 -1 + -7p + -4p2 = -10 + 10 Combine like terms: -10 + 10 = 0 -1 + -7p + -4p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 7p + 4p2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 7p + 4p2)' equal to zero and attempt to solve: Simplifying 1 + 7p + 4p2 = 0 Solving 1 + 7p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 1.75p + p2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.75p + -0.25 + p2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.75p + p2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.75p + p2 = 0 + -0.25 1.75p + p2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.75p + p2 = -0.25 The p term is 1.75p. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75p + 0.765625 + p2 = -0.25 + 0.765625 Reorder the terms: 0.765625 + 1.75p + p2 = -0.25 + 0.765625 Combine like terms: -0.25 + 0.765625 = 0.515625 0.765625 + 1.75p + p2 = 0.515625 Factor a perfect square on the left side: (p + 0.875)(p + 0.875) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (p + 0.875) equal to 0.718070331 and -0.718070331.Subproblem 1
p + 0.875 = 0.718070331 Simplifying p + 0.875 = 0.718070331 Reorder the terms: 0.875 + p = 0.718070331 Solving 0.875 + p = 0.718070331 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + p = 0.718070331 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + p = 0.718070331 + -0.875 p = 0.718070331 + -0.875 Combine like terms: 0.718070331 + -0.875 = -0.156929669 p = -0.156929669 Simplifying p = -0.156929669Subproblem 2
p + 0.875 = -0.718070331 Simplifying p + 0.875 = -0.718070331 Reorder the terms: 0.875 + p = -0.718070331 Solving 0.875 + p = -0.718070331 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + p = -0.718070331 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + p = -0.718070331 + -0.875 p = -0.718070331 + -0.875 Combine like terms: -0.718070331 + -0.875 = -1.593070331 p = -1.593070331 Simplifying p = -1.593070331Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.156929669, -1.593070331}Solution
p = {-0.156929669, -1.593070331}
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