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Simplifying 10p2 + -8p + -14 = 0 Reorder the terms: -14 + -8p + 10p2 = 0 Solving -14 + -8p + 10p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -4p + 5p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -4p + 5p2)' equal to zero and attempt to solve: Simplifying -7 + -4p + 5p2 = 0 Solving -7 + -4p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -0.8p + p2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.8p + 1.4 + p2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.8p + p2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.8p + p2 = 0 + 1.4 -0.8p + p2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.8p + p2 = 1.4 The p term is -0.8p. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8p + 0.16 + p2 = 1.4 + 0.16 Reorder the terms: 0.16 + -0.8p + p2 = 1.4 + 0.16 Combine like terms: 1.4 + 0.16 = 1.56 0.16 + -0.8p + p2 = 1.56 Factor a perfect square on the left side: (p + -0.4)(p + -0.4) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (p + -0.4) equal to 1.2489996 and -1.2489996.Subproblem 1
p + -0.4 = 1.2489996 Simplifying p + -0.4 = 1.2489996 Reorder the terms: -0.4 + p = 1.2489996 Solving -0.4 + p = 1.2489996 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + p = 1.2489996 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + p = 1.2489996 + 0.4 p = 1.2489996 + 0.4 Combine like terms: 1.2489996 + 0.4 = 1.6489996 p = 1.6489996 Simplifying p = 1.6489996Subproblem 2
p + -0.4 = -1.2489996 Simplifying p + -0.4 = -1.2489996 Reorder the terms: -0.4 + p = -1.2489996 Solving -0.4 + p = -1.2489996 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + p = -1.2489996 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + p = -1.2489996 + 0.4 p = -1.2489996 + 0.4 Combine like terms: -1.2489996 + 0.4 = -0.8489996 p = -0.8489996 Simplifying p = -0.8489996Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.6489996, -0.8489996}Solution
p = {1.6489996, -0.8489996}
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