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Simplifying 1.4r2 + -1.7r + 0.5 = 0 Reorder the terms: 0.5 + -1.7r + 1.4r2 = 0 Solving 0.5 + -1.7r + 1.4r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. 0.3571428571 + -1.214285714r + r2 = 0 Move the constant term to the right: Add '-0.3571428571' to each side of the equation. 0.3571428571 + -1.214285714r + -0.3571428571 + r2 = 0 + -0.3571428571 Reorder the terms: 0.3571428571 + -0.3571428571 + -1.214285714r + r2 = 0 + -0.3571428571 Combine like terms: 0.3571428571 + -0.3571428571 = 0.0000000000 0.0000000000 + -1.214285714r + r2 = 0 + -0.3571428571 -1.214285714r + r2 = 0 + -0.3571428571 Combine like terms: 0 + -0.3571428571 = -0.3571428571 -1.214285714r + r2 = -0.3571428571 The r term is -1.214285714r. Take half its coefficient (-0.607142857). Square it (0.3686224488) and add it to both sides. Add '0.3686224488' to each side of the equation. -1.214285714r + 0.3686224488 + r2 = -0.3571428571 + 0.3686224488 Reorder the terms: 0.3686224488 + -1.214285714r + r2 = -0.3571428571 + 0.3686224488 Combine like terms: -0.3571428571 + 0.3686224488 = 0.0114795917 0.3686224488 + -1.214285714r + r2 = 0.0114795917 Factor a perfect square on the left side: (r + -0.607142857)(r + -0.607142857) = 0.0114795917 Calculate the square root of the right side: 0.107142857 Break this problem into two subproblems by setting (r + -0.607142857) equal to 0.107142857 and -0.107142857.Subproblem 1
r + -0.607142857 = 0.107142857 Simplifying r + -0.607142857 = 0.107142857 Reorder the terms: -0.607142857 + r = 0.107142857 Solving -0.607142857 + r = 0.107142857 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.607142857' to each side of the equation. -0.607142857 + 0.607142857 + r = 0.107142857 + 0.607142857 Combine like terms: -0.607142857 + 0.607142857 = 0.000000000 0.000000000 + r = 0.107142857 + 0.607142857 r = 0.107142857 + 0.607142857 Combine like terms: 0.107142857 + 0.607142857 = 0.714285714 r = 0.714285714 Simplifying r = 0.714285714Subproblem 2
r + -0.607142857 = -0.107142857 Simplifying r + -0.607142857 = -0.107142857 Reorder the terms: -0.607142857 + r = -0.107142857 Solving -0.607142857 + r = -0.107142857 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.607142857' to each side of the equation. -0.607142857 + 0.607142857 + r = -0.107142857 + 0.607142857 Combine like terms: -0.607142857 + 0.607142857 = 0.000000000 0.000000000 + r = -0.107142857 + 0.607142857 r = -0.107142857 + 0.607142857 Combine like terms: -0.107142857 + 0.607142857 = 0.5 r = 0.5 Simplifying r = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.714285714, 0.5}
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