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Simplifying (x + -4) + -1x + 9 = (x + -4) * 6x Reorder the terms: (-4 + x) + -1x + 9 = (x + -4) * 6x Remove parenthesis around (-4 + x) -4 + x + -1x + 9 = (x + -4) * 6x Reorder the terms: -4 + 9 + x + -1x = (x + -4) * 6x Combine like terms: -4 + 9 = 5 5 + x + -1x = (x + -4) * 6x Combine like terms: x + -1x = 0 5 + 0 = (x + -4) * 6x 5 = (x + -4) * 6x Reorder the terms: 5 = (-4 + x) * 6x Reorder the terms for easier multiplication: 5 = 6x(-4 + x) 5 = (-4 * 6x + x * 6x) 5 = (-24x + 6x2) Solving 5 = -24x + 6x2 Solving for variable 'x'. Reorder the terms: 5 + 24x + -6x2 = -24x + 24x + 6x2 + -6x2 Combine like terms: -24x + 24x = 0 5 + 24x + -6x2 = 0 + 6x2 + -6x2 5 + 24x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 5 + 24x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.8333333333 + -4x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -4x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -4x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + 0.8333333333 -4x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -4x + x2 = 0.8333333333 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 = 0.8333333333 + 4 Reorder the terms: 4 + -4x + x2 = 0.8333333333 + 4 Combine like terms: 0.8333333333 + 4 = 4.8333333333 4 + -4x + x2 = 4.8333333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.8333333333 Calculate the square root of the right side: 2.198484326 Break this problem into two subproblems by setting (x + -2) equal to 2.198484326 and -2.198484326.Subproblem 1
x + -2 = 2.198484326 Simplifying x + -2 = 2.198484326 Reorder the terms: -2 + x = 2.198484326 Solving -2 + x = 2.198484326 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 = 2.198484326 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.198484326 + 2 x = 2.198484326 + 2 Combine like terms: 2.198484326 + 2 = 4.198484326 x = 4.198484326 Simplifying x = 4.198484326Subproblem 2
x + -2 = -2.198484326 Simplifying x + -2 = -2.198484326 Reorder the terms: -2 + x = -2.198484326 Solving -2 + x = -2.198484326 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 = -2.198484326 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.198484326 + 2 x = -2.198484326 + 2 Combine like terms: -2.198484326 + 2 = -0.198484326 x = -0.198484326 Simplifying x = -0.198484326Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.198484326, -0.198484326}
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