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Simplifying 36x = 4x2 + -50 Reorder the terms: 36x = -50 + 4x2 Solving 36x = -50 + 4x2 Solving for variable 'x'. Reorder the terms: 50 + 36x + -4x2 = -50 + 4x2 + 50 + -4x2 Reorder the terms: 50 + 36x + -4x2 = -50 + 50 + 4x2 + -4x2 Combine like terms: -50 + 50 = 0 50 + 36x + -4x2 = 0 + 4x2 + -4x2 50 + 36x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 50 + 36x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 18x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 18x + -2x2)' equal to zero and attempt to solve: Simplifying 25 + 18x + -2x2 = 0 Solving 25 + 18x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -12.5 + -9x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -9x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -9x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -9x + x2 = 0 + 12.5 -9x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -9x + x2 = 12.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 12.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 12.5 + 20.25 Combine like terms: 12.5 + 20.25 = 32.75 20.25 + -9x + x2 = 32.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 32.75 Calculate the square root of the right side: 5.722761571 Break this problem into two subproblems by setting (x + -4.5) equal to 5.722761571 and -5.722761571.Subproblem 1
x + -4.5 = 5.722761571 Simplifying x + -4.5 = 5.722761571 Reorder the terms: -4.5 + x = 5.722761571 Solving -4.5 + x = 5.722761571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.722761571 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.722761571 + 4.5 x = 5.722761571 + 4.5 Combine like terms: 5.722761571 + 4.5 = 10.222761571 x = 10.222761571 Simplifying x = 10.222761571Subproblem 2
x + -4.5 = -5.722761571 Simplifying x + -4.5 = -5.722761571 Reorder the terms: -4.5 + x = -5.722761571 Solving -4.5 + x = -5.722761571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.722761571 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.722761571 + 4.5 x = -5.722761571 + 4.5 Combine like terms: -5.722761571 + 4.5 = -1.222761571 x = -1.222761571 Simplifying x = -1.222761571Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.222761571, -1.222761571}Solution
x = {10.222761571, -1.222761571}
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