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Simplifying 6(N + -3) * 34N = 16 Reorder the terms: 6(-3 + N) * 34N = 16 Reorder the terms for easier multiplication: 6 * 34N(-3 + N) = 16 Multiply 6 * 34 204N(-3 + N) = 16 (-3 * 204N + N * 204N) = 16 (-612N + 204N2) = 16 Solving -612N + 204N2 = 16 Solving for variable 'N'. Reorder the terms: -16 + -612N + 204N2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -612N + 204N2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + -153N + 51N2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -153N + 51N2)' equal to zero and attempt to solve: Simplifying -4 + -153N + 51N2 = 0 Solving -4 + -153N + 51N2 = 0 Begin completing the square. Divide all terms by 51 the coefficient of the squared term: Divide each side by '51'. -0.07843137255 + -3N + N2 = 0 Move the constant term to the right: Add '0.07843137255' to each side of the equation. -0.07843137255 + -3N + 0.07843137255 + N2 = 0 + 0.07843137255 Reorder the terms: -0.07843137255 + 0.07843137255 + -3N + N2 = 0 + 0.07843137255 Combine like terms: -0.07843137255 + 0.07843137255 = 0.00000000000 0.00000000000 + -3N + N2 = 0 + 0.07843137255 -3N + N2 = 0 + 0.07843137255 Combine like terms: 0 + 0.07843137255 = 0.07843137255 -3N + N2 = 0.07843137255 The N term is -3N. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3N + 2.25 + N2 = 0.07843137255 + 2.25 Reorder the terms: 2.25 + -3N + N2 = 0.07843137255 + 2.25 Combine like terms: 0.07843137255 + 2.25 = 2.32843137255 2.25 + -3N + N2 = 2.32843137255 Factor a perfect square on the left side: (N + -1.5)(N + -1.5) = 2.32843137255 Calculate the square root of the right side: 1.525919845 Break this problem into two subproblems by setting (N + -1.5) equal to 1.525919845 and -1.525919845.Subproblem 1
N + -1.5 = 1.525919845 Simplifying N + -1.5 = 1.525919845 Reorder the terms: -1.5 + N = 1.525919845 Solving -1.5 + N = 1.525919845 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + N = 1.525919845 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + N = 1.525919845 + 1.5 N = 1.525919845 + 1.5 Combine like terms: 1.525919845 + 1.5 = 3.025919845 N = 3.025919845 Simplifying N = 3.025919845Subproblem 2
N + -1.5 = -1.525919845 Simplifying N + -1.5 = -1.525919845 Reorder the terms: -1.5 + N = -1.525919845 Solving -1.5 + N = -1.525919845 Solving for variable 'N'. Move all terms containing N to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + N = -1.525919845 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + N = -1.525919845 + 1.5 N = -1.525919845 + 1.5 Combine like terms: -1.525919845 + 1.5 = -0.025919845 N = -0.025919845 Simplifying N = -0.025919845Solution
The solution to the problem is based on the solutions from the subproblems. N = {3.025919845, -0.025919845}Solution
N = {3.025919845, -0.025919845}
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