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Simplifying -1x(x + -4) + 9 = 6x(x + -4) Reorder the terms: -1x(-4 + x) + 9 = 6x(x + -4) (-4 * -1x + x * -1x) + 9 = 6x(x + -4) (4x + -1x2) + 9 = 6x(x + -4) Reorder the terms: 9 + 4x + -1x2 = 6x(x + -4) Reorder the terms: 9 + 4x + -1x2 = 6x(-4 + x) 9 + 4x + -1x2 = (-4 * 6x + x * 6x) 9 + 4x + -1x2 = (-24x + 6x2) Solving 9 + 4x + -1x2 = -24x + 6x2 Solving for variable 'x'. Reorder the terms: 9 + 4x + 24x + -1x2 + -6x2 = -24x + 6x2 + 24x + -6x2 Combine like terms: 4x + 24x = 28x 9 + 28x + -1x2 + -6x2 = -24x + 6x2 + 24x + -6x2 Combine like terms: -1x2 + -6x2 = -7x2 9 + 28x + -7x2 = -24x + 6x2 + 24x + -6x2 Reorder the terms: 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 = 5.285714286 4 + -4x + x2 = 5.285714286 Factor a perfect square on the left side: (x + -2)(x + -2) = 5.285714286 Calculate the square root of the right side: 2.299068134 Break this problem into two subproblems by setting (x + -2) equal to 2.299068134 and -2.299068134.Subproblem 1
x + -2 = 2.299068134 Simplifying x + -2 = 2.299068134 Reorder the terms: -2 + x = 2.299068134 Solving -2 + x = 2.299068134 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 = 2.299068134 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.299068134 + 2 x = 2.299068134 + 2 Combine like terms: 2.299068134 + 2 = 4.299068134 x = 4.299068134 Simplifying x = 4.299068134Subproblem 2
x + -2 = -2.299068134 Simplifying x + -2 = -2.299068134 Reorder the terms: -2 + x = -2.299068134 Solving -2 + x = -2.299068134 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 = -2.299068134 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.299068134 + 2 x = -2.299068134 + 2 Combine like terms: -2.299068134 + 2 = -0.299068134 x = -0.299068134 Simplifying x = -0.299068134Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.299068134, -0.299068134}
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