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Simplifying 34k2 + -24k = 3 Reorder the terms: -24k + 34k2 = 3 Solving -24k + 34k2 = 3 Solving for variable 'k'. Reorder the terms: -3 + -24k + 34k2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -24k + 34k2 = 0 Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. -0.08823529412 + -0.7058823529k + k2 = 0 Move the constant term to the right: Add '0.08823529412' to each side of the equation. -0.08823529412 + -0.7058823529k + 0.08823529412 + k2 = 0 + 0.08823529412 Reorder the terms: -0.08823529412 + 0.08823529412 + -0.7058823529k + k2 = 0 + 0.08823529412 Combine like terms: -0.08823529412 + 0.08823529412 = 0.00000000000 0.00000000000 + -0.7058823529k + k2 = 0 + 0.08823529412 -0.7058823529k + k2 = 0 + 0.08823529412 Combine like terms: 0 + 0.08823529412 = 0.08823529412 -0.7058823529k + k2 = 0.08823529412 The k term is -0.7058823529k. Take half its coefficient (-0.3529411765). Square it (0.1245674741) and add it to both sides. Add '0.1245674741' to each side of the equation. -0.7058823529k + 0.1245674741 + k2 = 0.08823529412 + 0.1245674741 Reorder the terms: 0.1245674741 + -0.7058823529k + k2 = 0.08823529412 + 0.1245674741 Combine like terms: 0.08823529412 + 0.1245674741 = 0.21280276822 0.1245674741 + -0.7058823529k + k2 = 0.21280276822 Factor a perfect square on the left side: (k + -0.3529411765)(k + -0.3529411765) = 0.21280276822 Calculate the square root of the right side: 0.461305504 Break this problem into two subproblems by setting (k + -0.3529411765) equal to 0.461305504 and -0.461305504.Subproblem 1
k + -0.3529411765 = 0.461305504 Simplifying k + -0.3529411765 = 0.461305504 Reorder the terms: -0.3529411765 + k = 0.461305504 Solving -0.3529411765 + k = 0.461305504 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.3529411765' to each side of the equation. -0.3529411765 + 0.3529411765 + k = 0.461305504 + 0.3529411765 Combine like terms: -0.3529411765 + 0.3529411765 = 0.0000000000 0.0000000000 + k = 0.461305504 + 0.3529411765 k = 0.461305504 + 0.3529411765 Combine like terms: 0.461305504 + 0.3529411765 = 0.8142466805 k = 0.8142466805 Simplifying k = 0.8142466805Subproblem 2
k + -0.3529411765 = -0.461305504 Simplifying k + -0.3529411765 = -0.461305504 Reorder the terms: -0.3529411765 + k = -0.461305504 Solving -0.3529411765 + k = -0.461305504 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.3529411765' to each side of the equation. -0.3529411765 + 0.3529411765 + k = -0.461305504 + 0.3529411765 Combine like terms: -0.3529411765 + 0.3529411765 = 0.0000000000 0.0000000000 + k = -0.461305504 + 0.3529411765 k = -0.461305504 + 0.3529411765 Combine like terms: -0.461305504 + 0.3529411765 = -0.1083643275 k = -0.1083643275 Simplifying k = -0.1083643275Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.8142466805, -0.1083643275}
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