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Simplifying 91 = (4 + x) * x Reorder the terms for easier multiplication: 91 = x(4 + x) 91 = (4 * x + x * x) 91 = (4x + x2) Solving 91 = 4x + x2 Solving for variable 'x'. Reorder the terms: 91 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 91 + -4x + -1x2 = 0 + x2 + -1x2 91 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 91 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -91 + 4x + x2 = 0 Move the constant term to the right: Add '91' to each side of the equation. -91 + 4x + 91 + x2 = 0 + 91 Reorder the terms: -91 + 91 + 4x + x2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 4x + x2 = 0 + 91 4x + x2 = 0 + 91 Combine like terms: 0 + 91 = 91 4x + x2 = 91 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 91 + 4 Reorder the terms: 4 + 4x + x2 = 91 + 4 Combine like terms: 91 + 4 = 95 4 + 4x + x2 = 95 Factor a perfect square on the left side: (x + 2)(x + 2) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (x + 2) equal to 9.746794345 and -9.746794345.Subproblem 1
x + 2 = 9.746794345 Simplifying x + 2 = 9.746794345 Reorder the terms: 2 + x = 9.746794345 Solving 2 + x = 9.746794345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.746794345 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.746794345 + -2 x = 9.746794345 + -2 Combine like terms: 9.746794345 + -2 = 7.746794345 x = 7.746794345 Simplifying x = 7.746794345Subproblem 2
x + 2 = -9.746794345 Simplifying x + 2 = -9.746794345 Reorder the terms: 2 + x = -9.746794345 Solving 2 + x = -9.746794345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.746794345 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.746794345 + -2 x = -9.746794345 + -2 Combine like terms: -9.746794345 + -2 = -11.746794345 x = -11.746794345 Simplifying x = -11.746794345Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.746794345, -11.746794345}
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