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Simplifying -1x(x + -4) = 6x(x + -4) + 9 Reorder the terms: -1x(-4 + x) = 6x(x + -4) + 9 (-4 * -1x + x * -1x) = 6x(x + -4) + 9 (4x + -1x2) = 6x(x + -4) + 9 Reorder the terms: 4x + -1x2 = 6x(-4 + x) + 9 4x + -1x2 = (-4 * 6x + x * 6x) + 9 4x + -1x2 = (-24x + 6x2) + 9 Reorder the terms: 4x + -1x2 = 9 + -24x + 6x2 Solving 4x + -1x2 = 9 + -24x + 6x2 Solving for variable 'x'. Reorder the terms: -9 + 4x + 24x + -1x2 + -6x2 = 9 + -24x + 6x2 + -9 + 24x + -6x2 Combine like terms: 4x + 24x = 28x -9 + 28x + -1x2 + -6x2 = 9 + -24x + 6x2 + -9 + 24x + -6x2 Combine like terms: -1x2 + -6x2 = -7x2 -9 + 28x + -7x2 = 9 + -24x + 6x2 + -9 + 24x + -6x2 Reorder the terms: -9 + 28x + -7x2 = 9 + -9 + -24x + 24x + 6x2 + -6x2 Combine like terms: 9 + -9 = 0 -9 + 28x + -7x2 = 0 + -24x + 24x + 6x2 + -6x2 -9 + 28x + -7x2 = -24x + 24x + 6x2 + -6x2 Combine like terms: -24x + 24x = 0 -9 + 28x + -7x2 = 0 + 6x2 + -6x2 -9 + 28x + -7x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -9 + 28x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 1.285714286 + -4x + x2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + -4x + -1.285714286 + x2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + -4x + x2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + -4x + x2 = 0 + -1.285714286 -4x + x2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 -4x + x2 = -1.285714286 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 = -1.285714286 + 4 Reorder the terms: 4 + -4x + x2 = -1.285714286 + 4 Combine like terms: -1.285714286 + 4 = 2.714285714 4 + -4x + x2 = 2.714285714 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.714285714 Calculate the square root of the right side: 1.647508942 Break this problem into two subproblems by setting (x + -2) equal to 1.647508942 and -1.647508942.Subproblem 1
x + -2 = 1.647508942 Simplifying x + -2 = 1.647508942 Reorder the terms: -2 + x = 1.647508942 Solving -2 + x = 1.647508942 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 = 1.647508942 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.647508942 + 2 x = 1.647508942 + 2 Combine like terms: 1.647508942 + 2 = 3.647508942 x = 3.647508942 Simplifying x = 3.647508942Subproblem 2
x + -2 = -1.647508942 Simplifying x + -2 = -1.647508942 Reorder the terms: -2 + x = -1.647508942 Solving -2 + x = -1.647508942 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 = -1.647508942 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.647508942 + 2 x = -1.647508942 + 2 Combine like terms: -1.647508942 + 2 = 0.352491058 x = 0.352491058 Simplifying x = 0.352491058Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.647508942, 0.352491058}
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