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Simplifying 2x + -3 = -6x + 4 + 22(x + -3)(x + 4) Reorder the terms: -3 + 2x = -6x + 4 + 22(x + -3)(x + 4) Reorder the terms: -3 + 2x = -6x + 4 + 22(-3 + x)(x + 4) Reorder the terms: -3 + 2x = -6x + 4 + 22(-3 + x)(4 + x) Multiply (-3 + x) * (4 + x) -3 + 2x = -6x + 4 + 22(-3(4 + x) + x(4 + x)) -3 + 2x = -6x + 4 + 22((4 * -3 + x * -3) + x(4 + x)) -3 + 2x = -6x + 4 + 22((-12 + -3x) + x(4 + x)) -3 + 2x = -6x + 4 + 22(-12 + -3x + (4 * x + x * x)) -3 + 2x = -6x + 4 + 22(-12 + -3x + (4x + x2)) Combine like terms: -3x + 4x = 1x -3 + 2x = -6x + 4 + 22(-12 + 1x + x2) -3 + 2x = -6x + 4 + (-12 * 22 + 1x * 22 + x2 * 22) -3 + 2x = -6x + 4 + (-264 + 22x + 22x2) Reorder the terms: -3 + 2x = 4 + -264 + -6x + 22x + 22x2 Combine like terms: 4 + -264 = -260 -3 + 2x = -260 + -6x + 22x + 22x2 Combine like terms: -6x + 22x = 16x -3 + 2x = -260 + 16x + 22x2 Solving -3 + 2x = -260 + 16x + 22x2 Solving for variable 'x'. Reorder the terms: -3 + 260 + 2x + -16x + -22x2 = -260 + 16x + 22x2 + 260 + -16x + -22x2 Combine like terms: -3 + 260 = 257 257 + 2x + -16x + -22x2 = -260 + 16x + 22x2 + 260 + -16x + -22x2 Combine like terms: 2x + -16x = -14x 257 + -14x + -22x2 = -260 + 16x + 22x2 + 260 + -16x + -22x2 Reorder the terms: 257 + -14x + -22x2 = -260 + 260 + 16x + -16x + 22x2 + -22x2 Combine like terms: -260 + 260 = 0 257 + -14x + -22x2 = 0 + 16x + -16x + 22x2 + -22x2 257 + -14x + -22x2 = 16x + -16x + 22x2 + -22x2 Combine like terms: 16x + -16x = 0 257 + -14x + -22x2 = 0 + 22x2 + -22x2 257 + -14x + -22x2 = 22x2 + -22x2 Combine like terms: 22x2 + -22x2 = 0 257 + -14x + -22x2 = 0 Begin completing the square. Divide all terms by -22 the coefficient of the squared term: Divide each side by '-22'. -11.68181818 + 0.6363636364x + x2 = 0 Move the constant term to the right: Add '11.68181818' to each side of the equation. -11.68181818 + 0.6363636364x + 11.68181818 + x2 = 0 + 11.68181818 Reorder the terms: -11.68181818 + 11.68181818 + 0.6363636364x + x2 = 0 + 11.68181818 Combine like terms: -11.68181818 + 11.68181818 = 0.00000000 0.00000000 + 0.6363636364x + x2 = 0 + 11.68181818 0.6363636364x + x2 = 0 + 11.68181818 Combine like terms: 0 + 11.68181818 = 11.68181818 0.6363636364x + x2 = 11.68181818 The x term is 0.6363636364x. Take half its coefficient (0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. 0.6363636364x + 0.1012396694 + x2 = 11.68181818 + 0.1012396694 Reorder the terms: 0.1012396694 + 0.6363636364x + x2 = 11.68181818 + 0.1012396694 Combine like terms: 11.68181818 + 0.1012396694 = 11.7830578494 0.1012396694 + 0.6363636364x + x2 = 11.7830578494 Factor a perfect square on the left side: (x + 0.3181818182)(x + 0.3181818182) = 11.7830578494 Calculate the square root of the right side: 3.432645896 Break this problem into two subproblems by setting (x + 0.3181818182) equal to 3.432645896 and -3.432645896.Subproblem 1
x + 0.3181818182 = 3.432645896 Simplifying x + 0.3181818182 = 3.432645896 Reorder the terms: 0.3181818182 + x = 3.432645896 Solving 0.3181818182 + x = 3.432645896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3181818182' to each side of the equation. 0.3181818182 + -0.3181818182 + x = 3.432645896 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + x = 3.432645896 + -0.3181818182 x = 3.432645896 + -0.3181818182 Combine like terms: 3.432645896 + -0.3181818182 = 3.1144640778 x = 3.1144640778 Simplifying x = 3.1144640778Subproblem 2
x + 0.3181818182 = -3.432645896 Simplifying x + 0.3181818182 = -3.432645896 Reorder the terms: 0.3181818182 + x = -3.432645896 Solving 0.3181818182 + x = -3.432645896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3181818182' to each side of the equation. 0.3181818182 + -0.3181818182 + x = -3.432645896 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + x = -3.432645896 + -0.3181818182 x = -3.432645896 + -0.3181818182 Combine like terms: -3.432645896 + -0.3181818182 = -3.7508277142 x = -3.7508277142 Simplifying x = -3.7508277142Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1144640778, -3.7508277142}
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