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Simplifying 5x + -1[3(x + -4)][7x + -4(x + 3)] = 0 Reorder the terms: 5x + -1[3(-4 + x)][7x + -4(x + 3)] = 0 5x + -1[(-4 * 3 + x * 3)][7x + -4(x + 3)] = 0 5x + -1[(-12 + 3x)][7x + -4(x + 3)] = 0 Reorder the terms: 5x + -1[-12 + 3x][7x + -4(3 + x)] = 0 5x + -1[-12 + 3x][7x + (3 * -4 + x * -4)] = 0 5x + -1[-12 + 3x][7x + (-12 + -4x)] = 0 Reorder the terms: 5x + -1[-12 + 3x][-12 + 7x + -4x] = 0 Combine like terms: 7x + -4x = 3x 5x + -1[-12 + 3x][-12 + 3x] = 0 Multiply [-12 + 3x] * [-12 + 3x] 5x + -1[-12[-12 + 3x] + 3x * [-12 + 3x]] = 0 5x + -1[[-12 * -12 + 3x * -12] + 3x * [-12 + 3x]] = 0 5x + -1[[144 + -36x] + 3x * [-12 + 3x]] = 0 5x + -1[144 + -36x + [-12 * 3x + 3x * 3x]] = 0 5x + -1[144 + -36x + [-36x + 9x2]] = 0 Combine like terms: -36x + -36x = -72x 5x + -1[144 + -72x + 9x2] = 0 5x + [144 * -1 + -72x * -1 + 9x2 * -1] = 0 5x + [-144 + 72x + -9x2] = 0 Reorder the terms: -144 + 5x + 72x + -9x2 = 0 Combine like terms: 5x + 72x = 77x -144 + 77x + -9x2 = 0 Solving -144 + 77x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 16 + -8.555555556x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -8.555555556x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -8.555555556x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -8.555555556x + x2 = 0 + -16 -8.555555556x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -8.555555556x + x2 = -16 The x term is -8.555555556x. Take half its coefficient (-4.277777778). Square it (18.29938272) and add it to both sides. Add '18.29938272' to each side of the equation. -8.555555556x + 18.29938272 + x2 = -16 + 18.29938272 Reorder the terms: 18.29938272 + -8.555555556x + x2 = -16 + 18.29938272 Combine like terms: -16 + 18.29938272 = 2.29938272 18.29938272 + -8.555555556x + x2 = 2.29938272 Factor a perfect square on the left side: (x + -4.277777778)(x + -4.277777778) = 2.29938272 Calculate the square root of the right side: 1.516371564 Break this problem into two subproblems by setting (x + -4.277777778) equal to 1.516371564 and -1.516371564.Subproblem 1
x + -4.277777778 = 1.516371564 Simplifying x + -4.277777778 = 1.516371564 Reorder the terms: -4.277777778 + x = 1.516371564 Solving -4.277777778 + x = 1.516371564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.277777778' to each side of the equation. -4.277777778 + 4.277777778 + x = 1.516371564 + 4.277777778 Combine like terms: -4.277777778 + 4.277777778 = 0.000000000 0.000000000 + x = 1.516371564 + 4.277777778 x = 1.516371564 + 4.277777778 Combine like terms: 1.516371564 + 4.277777778 = 5.794149342 x = 5.794149342 Simplifying x = 5.794149342Subproblem 2
x + -4.277777778 = -1.516371564 Simplifying x + -4.277777778 = -1.516371564 Reorder the terms: -4.277777778 + x = -1.516371564 Solving -4.277777778 + x = -1.516371564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.277777778' to each side of the equation. -4.277777778 + 4.277777778 + x = -1.516371564 + 4.277777778 Combine like terms: -4.277777778 + 4.277777778 = 0.000000000 0.000000000 + x = -1.516371564 + 4.277777778 x = -1.516371564 + 4.277777778 Combine like terms: -1.516371564 + 4.277777778 = 2.761406214 x = 2.761406214 Simplifying x = 2.761406214Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.794149342, 2.761406214}
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