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Simplifying 35k2 + -32k + 7 = 4 Reorder the terms: 7 + -32k + 35k2 = 4 Solving 7 + -32k + 35k2 = 4 Solving for variable 'k'. Reorder the terms: 7 + -4 + -32k + 35k2 = 4 + -4 Combine like terms: 7 + -4 = 3 3 + -32k + 35k2 = 4 + -4 Combine like terms: 4 + -4 = 0 3 + -32k + 35k2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.08571428571 + -0.9142857143k + k2 = 0 Move the constant term to the right: Add '-0.08571428571' to each side of the equation. 0.08571428571 + -0.9142857143k + -0.08571428571 + k2 = 0 + -0.08571428571 Reorder the terms: 0.08571428571 + -0.08571428571 + -0.9142857143k + k2 = 0 + -0.08571428571 Combine like terms: 0.08571428571 + -0.08571428571 = 0.00000000000 0.00000000000 + -0.9142857143k + k2 = 0 + -0.08571428571 -0.9142857143k + k2 = 0 + -0.08571428571 Combine like terms: 0 + -0.08571428571 = -0.08571428571 -0.9142857143k + k2 = -0.08571428571 The k term is -0.9142857143k. Take half its coefficient (-0.4571428572). Square it (0.2089795919) and add it to both sides. Add '0.2089795919' to each side of the equation. -0.9142857143k + 0.2089795919 + k2 = -0.08571428571 + 0.2089795919 Reorder the terms: 0.2089795919 + -0.9142857143k + k2 = -0.08571428571 + 0.2089795919 Combine like terms: -0.08571428571 + 0.2089795919 = 0.12326530619 0.2089795919 + -0.9142857143k + k2 = 0.12326530619 Factor a perfect square on the left side: (k + -0.4571428572)(k + -0.4571428572) = 0.12326530619 Calculate the square root of the right side: 0.351091592 Break this problem into two subproblems by setting (k + -0.4571428572) equal to 0.351091592 and -0.351091592.Subproblem 1
k + -0.4571428572 = 0.351091592 Simplifying k + -0.4571428572 = 0.351091592 Reorder the terms: -0.4571428572 + k = 0.351091592 Solving -0.4571428572 + k = 0.351091592 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.4571428572' to each side of the equation. -0.4571428572 + 0.4571428572 + k = 0.351091592 + 0.4571428572 Combine like terms: -0.4571428572 + 0.4571428572 = 0.0000000000 0.0000000000 + k = 0.351091592 + 0.4571428572 k = 0.351091592 + 0.4571428572 Combine like terms: 0.351091592 + 0.4571428572 = 0.8082344492 k = 0.8082344492 Simplifying k = 0.8082344492Subproblem 2
k + -0.4571428572 = -0.351091592 Simplifying k + -0.4571428572 = -0.351091592 Reorder the terms: -0.4571428572 + k = -0.351091592 Solving -0.4571428572 + k = -0.351091592 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.4571428572' to each side of the equation. -0.4571428572 + 0.4571428572 + k = -0.351091592 + 0.4571428572 Combine like terms: -0.4571428572 + 0.4571428572 = 0.0000000000 0.0000000000 + k = -0.351091592 + 0.4571428572 k = -0.351091592 + 0.4571428572 Combine like terms: -0.351091592 + 0.4571428572 = 0.1060512652 k = 0.1060512652 Simplifying k = 0.1060512652Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.8082344492, 0.1060512652}
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