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Simplifying 10p2 + -6p + -14 = 0 Reorder the terms: -14 + -6p + 10p2 = 0 Solving -14 + -6p + 10p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + -3p + 5p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -3p + 5p2)' equal to zero and attempt to solve: Simplifying -7 + -3p + 5p2 = 0 Solving -7 + -3p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -0.6p + p2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.6p + 1.4 + p2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.6p + p2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.6p + p2 = 0 + 1.4 -0.6p + p2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.6p + p2 = 1.4 The p term is -0.6p. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6p + 0.09 + p2 = 1.4 + 0.09 Reorder the terms: 0.09 + -0.6p + p2 = 1.4 + 0.09 Combine like terms: 1.4 + 0.09 = 1.49 0.09 + -0.6p + p2 = 1.49 Factor a perfect square on the left side: (p + -0.3)(p + -0.3) = 1.49 Calculate the square root of the right side: 1.220655562 Break this problem into two subproblems by setting (p + -0.3) equal to 1.220655562 and -1.220655562.Subproblem 1
p + -0.3 = 1.220655562 Simplifying p + -0.3 = 1.220655562 Reorder the terms: -0.3 + p = 1.220655562 Solving -0.3 + p = 1.220655562 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + p = 1.220655562 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + p = 1.220655562 + 0.3 p = 1.220655562 + 0.3 Combine like terms: 1.220655562 + 0.3 = 1.520655562 p = 1.520655562 Simplifying p = 1.520655562Subproblem 2
p + -0.3 = -1.220655562 Simplifying p + -0.3 = -1.220655562 Reorder the terms: -0.3 + p = -1.220655562 Solving -0.3 + p = -1.220655562 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + p = -1.220655562 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + p = -1.220655562 + 0.3 p = -1.220655562 + 0.3 Combine like terms: -1.220655562 + 0.3 = -0.920655562 p = -0.920655562 Simplifying p = -0.920655562Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.520655562, -0.920655562}Solution
p = {1.520655562, -0.920655562}
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