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Simplifying 36x + 11 = 5x2 Reorder the terms: 11 + 36x = 5x2 Solving 11 + 36x = 5x2 Solving for variable 'x'. Combine like terms: 5x2 + -5x2 = 0 11 + 36x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.2 + -7.2x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -7.2x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -7.2x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -7.2x + x2 = 0 + 2.2 -7.2x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -7.2x + x2 = 2.2 The x term is -7.2x. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2x + 12.96 + x2 = 2.2 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = 2.2 + 12.96 Combine like terms: 2.2 + 12.96 = 15.16 12.96 + -7.2x + x2 = 15.16 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 15.16 Calculate the square root of the right side: 3.893584467 Break this problem into two subproblems by setting (x + -3.6) equal to 3.893584467 and -3.893584467.Subproblem 1
x + -3.6 = 3.893584467 Simplifying x + -3.6 = 3.893584467 Reorder the terms: -3.6 + x = 3.893584467 Solving -3.6 + x = 3.893584467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 3.893584467 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 3.893584467 + 3.6 x = 3.893584467 + 3.6 Combine like terms: 3.893584467 + 3.6 = 7.493584467 x = 7.493584467 Simplifying x = 7.493584467Subproblem 2
x + -3.6 = -3.893584467 Simplifying x + -3.6 = -3.893584467 Reorder the terms: -3.6 + x = -3.893584467 Solving -3.6 + x = -3.893584467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -3.893584467 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -3.893584467 + 3.6 x = -3.893584467 + 3.6 Combine like terms: -3.893584467 + 3.6 = -0.293584467 x = -0.293584467 Simplifying x = -0.293584467Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.493584467, -0.293584467}
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