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Simplifying 10p2 + p = 6 Reorder the terms: p + 10p2 = 6 Solving p + 10p2 = 6 Solving for variable 'p'. Reorder the terms: -6 + p + 10p2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + p + 10p2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.6 + 0.1p + p2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 0.1p + 0.6 + p2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 0.1p + p2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 0.1p + p2 = 0 + 0.6 0.1p + p2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 0.1p + p2 = 0.6 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1p + 0.25 + p2 = 0.6 + 0.25 Reorder the terms: 0.25 + 0.1p + p2 = 0.6 + 0.25 Combine like terms: 0.6 + 0.25 = 0.85 0.25 + 0.1p + p2 = 0.85 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 0.85 Calculate the square root of the right side: 0.921954446 Break this problem into two subproblems by setting (p + 0.5) equal to 0.921954446 and -0.921954446.Subproblem 1
p + 0.5 = 0.921954446 Simplifying p + 0.5 = 0.921954446 Reorder the terms: 0.5 + p = 0.921954446 Solving 0.5 + p = 0.921954446 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 0.921954446 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 0.921954446 + -0.5 p = 0.921954446 + -0.5 Combine like terms: 0.921954446 + -0.5 = 0.421954446 p = 0.421954446 Simplifying p = 0.421954446Subproblem 2
p + 0.5 = -0.921954446 Simplifying p + 0.5 = -0.921954446 Reorder the terms: 0.5 + p = -0.921954446 Solving 0.5 + p = -0.921954446 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -0.921954446 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -0.921954446 + -0.5 p = -0.921954446 + -0.5 Combine like terms: -0.921954446 + -0.5 = -1.421954446 p = -1.421954446 Simplifying p = -1.421954446Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.421954446, -1.421954446}
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