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Simplifying (-4x2) + 68x = 144 Reorder the terms: 68x + (-4x2) = 144 Solving 68x + (-4x2) = 144 Solving for variable 'x'. Reorder the terms: -144 + 68x + (-4x2) = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 68x + (-4x2) = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-36 + 17x + (-1x2)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-36 + 17x + (-1x2))' equal to zero and attempt to solve: Simplifying -36 + 17x + (-1x2) = 0 Solving -36 + 17x + (-1x2) = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 36 + -17x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + -17x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -17x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -17x + x2 = 0 + -36 -17x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -17x + x2 = -36 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -36 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -36 + 72.25 Combine like terms: -36 + 72.25 = 36.25 72.25 + -17x + x2 = 36.25 Factor a perfect square on the left side: ((x) + -8.5)((x) + -8.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting ((x) + -8.5) equal to 6.020797289 and -6.020797289.Subproblem 1
(x) + -8.5 = 6.020797289 Simplifying (x) + -8.5 = 6.020797289 x + -8.5 = 6.020797289 Reorder the terms: -8.5 + x = 6.020797289 Solving -8.5 + x = 6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 6.020797289 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 6.020797289 + 8.5 x = 6.020797289 + 8.5 Combine like terms: 6.020797289 + 8.5 = 14.520797289 x = 14.520797289 Simplifying x = 14.520797289Subproblem 2
(x) + -8.5 = -6.020797289 Simplifying (x) + -8.5 = -6.020797289 x + -8.5 = -6.020797289 Reorder the terms: -8.5 + x = -6.020797289 Solving -8.5 + x = -6.020797289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -6.020797289 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -6.020797289 + 8.5 x = -6.020797289 + 8.5 Combine like terms: -6.020797289 + 8.5 = 2.479202711 x = 2.479202711 Simplifying x = 2.479202711Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.520797289, 2.479202711}Solution
x = {14.520797289, 2.479202711}
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