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Simplifying 6k2 + 84k = 270 Reorder the terms: 84k + 6k2 = 270 Solving 84k + 6k2 = 270 Solving for variable 'k'. Reorder the terms: -270 + 84k + 6k2 = 270 + -270 Combine like terms: 270 + -270 = 0 -270 + 84k + 6k2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-45 + 14k + k2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-45 + 14k + k2)' equal to zero and attempt to solve: Simplifying -45 + 14k + k2 = 0 Solving -45 + 14k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 14k + 45 + k2 = 0 + 45 Reorder the terms: -45 + 45 + 14k + k2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 14k + k2 = 0 + 45 14k + k2 = 0 + 45 Combine like terms: 0 + 45 = 45 14k + k2 = 45 The k term is 14k. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14k + 49 + k2 = 45 + 49 Reorder the terms: 49 + 14k + k2 = 45 + 49 Combine like terms: 45 + 49 = 94 49 + 14k + k2 = 94 Factor a perfect square on the left side: (k + 7)(k + 7) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (k + 7) equal to 9.695359715 and -9.695359715.Subproblem 1
k + 7 = 9.695359715 Simplifying k + 7 = 9.695359715 Reorder the terms: 7 + k = 9.695359715 Solving 7 + k = 9.695359715 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + k = 9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + k = 9.695359715 + -7 k = 9.695359715 + -7 Combine like terms: 9.695359715 + -7 = 2.695359715 k = 2.695359715 Simplifying k = 2.695359715Subproblem 2
k + 7 = -9.695359715 Simplifying k + 7 = -9.695359715 Reorder the terms: 7 + k = -9.695359715 Solving 7 + k = -9.695359715 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + k = -9.695359715 + -7 Combine like terms: 7 + -7 = 0 0 + k = -9.695359715 + -7 k = -9.695359715 + -7 Combine like terms: -9.695359715 + -7 = -16.695359715 k = -16.695359715 Simplifying k = -16.695359715Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.695359715, -16.695359715}Solution
k = {2.695359715, -16.695359715}
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