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Simplifying x(x + -4) = 91 Reorder the terms: x(-4 + x) = 91 (-4 * x + x * x) = 91 (-4x + x2) = 91 Solving -4x + x2 = 91 Solving for variable 'x'. Reorder the terms: -91 + -4x + x2 = 91 + -91 Combine like terms: 91 + -91 = 0 -91 + -4x + x2 = 0 Begin completing the square. 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 = 11.746794345 x = 11.746794345 Simplifying x = 11.746794345Subproblem 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 = -7.746794345 x = -7.746794345 Simplifying x = -7.746794345Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.746794345, -7.746794345}
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