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Simplifying 6x + 4x + -2 + 2(4x + -42) * x + -4 = 50 Reorder the terms: 6x + 4x + -2 + 2(-42 + 4x) * x + -4 = 50 Reorder the terms for easier multiplication: 6x + 4x + -2 + 2x(-42 + 4x) + -4 = 50 6x + 4x + -2 + (-42 * 2x + 4x * 2x) + -4 = 50 6x + 4x + -2 + (-84x + 8x2) + -4 = 50 Reorder the terms: -2 + -4 + 6x + 4x + -84x + 8x2 = 50 Combine like terms: -2 + -4 = -6 -6 + 6x + 4x + -84x + 8x2 = 50 Combine like terms: 6x + 4x = 10x -6 + 10x + -84x + 8x2 = 50 Combine like terms: 10x + -84x = -74x -6 + -74x + 8x2 = 50 Solving -6 + -74x + 8x2 = 50 Solving for variable 'x'. Reorder the terms: -6 + -50 + -74x + 8x2 = 50 + -50 Combine like terms: -6 + -50 = -56 -56 + -74x + 8x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -56 + -74x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + -37x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + -37x + 4x2)' equal to zero and attempt to solve: Simplifying -28 + -37x + 4x2 = 0 Solving -28 + -37x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7 + -9.25x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -9.25x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -9.25x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -9.25x + x2 = 0 + 7 -9.25x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -9.25x + x2 = 7 The x term is -9.25x. Take half its coefficient (-4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. -9.25x + 21.390625 + x2 = 7 + 21.390625 Reorder the terms: 21.390625 + -9.25x + x2 = 7 + 21.390625 Combine like terms: 7 + 21.390625 = 28.390625 21.390625 + -9.25x + x2 = 28.390625 Factor a perfect square on the left side: (x + -4.625)(x + -4.625) = 28.390625 Calculate the square root of the right side: 5.328285371 Break this problem into two subproblems by setting (x + -4.625) equal to 5.328285371 and -5.328285371.Subproblem 1
x + -4.625 = 5.328285371 Simplifying x + -4.625 = 5.328285371 Reorder the terms: -4.625 + x = 5.328285371 Solving -4.625 + x = 5.328285371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = 5.328285371 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = 5.328285371 + 4.625 x = 5.328285371 + 4.625 Combine like terms: 5.328285371 + 4.625 = 9.953285371 x = 9.953285371 Simplifying x = 9.953285371Subproblem 2
x + -4.625 = -5.328285371 Simplifying x + -4.625 = -5.328285371 Reorder the terms: -4.625 + x = -5.328285371 Solving -4.625 + x = -5.328285371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = -5.328285371 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = -5.328285371 + 4.625 x = -5.328285371 + 4.625 Combine like terms: -5.328285371 + 4.625 = -0.703285371 x = -0.703285371 Simplifying x = -0.703285371Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.953285371, -0.703285371}Solution
x = {9.953285371, -0.703285371}
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