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Simplifying [6x + 2][3x + -14] = 8x + 4 Reorder the terms: [2 + 6x][3x + -14] = 8x + 4 Reorder the terms: [2 + 6x][-14 + 3x] = 8x + 4 Multiply [2 + 6x] * [-14 + 3x] [2[-14 + 3x] + 6x * [-14 + 3x]] = 8x + 4 [[-14 * 2 + 3x * 2] + 6x * [-14 + 3x]] = 8x + 4 [[-28 + 6x] + 6x * [-14 + 3x]] = 8x + 4 [-28 + 6x + [-14 * 6x + 3x * 6x]] = 8x + 4 [-28 + 6x + [-84x + 18x2]] = 8x + 4 Combine like terms: 6x + -84x = -78x [-28 + -78x + 18x2] = 8x + 4 Reorder the terms: -28 + -78x + 18x2 = 4 + 8x Solving -28 + -78x + 18x2 = 4 + 8x Solving for variable 'x'. Reorder the terms: -28 + -4 + -78x + -8x + 18x2 = 4 + 8x + -4 + -8x Combine like terms: -28 + -4 = -32 -32 + -78x + -8x + 18x2 = 4 + 8x + -4 + -8x Combine like terms: -78x + -8x = -86x -32 + -86x + 18x2 = 4 + 8x + -4 + -8x Reorder the terms: -32 + -86x + 18x2 = 4 + -4 + 8x + -8x Combine like terms: 4 + -4 = 0 -32 + -86x + 18x2 = 0 + 8x + -8x -32 + -86x + 18x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -32 + -86x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -43x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -43x + 9x2)' equal to zero and attempt to solve: Simplifying -16 + -43x + 9x2 = 0 Solving -16 + -43x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + -4.777777778x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -4.777777778x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -4.777777778x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -4.777777778x + x2 = 0 + 1.777777778 -4.777777778x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -4.777777778x + x2 = 1.777777778 The x term is -4.777777778x. Take half its coefficient (-2.388888889). Square it (5.706790124) and add it to both sides. Add '5.706790124' to each side of the equation. -4.777777778x + 5.706790124 + x2 = 1.777777778 + 5.706790124 Reorder the terms: 5.706790124 + -4.777777778x + x2 = 1.777777778 + 5.706790124 Combine like terms: 1.777777778 + 5.706790124 = 7.484567902 5.706790124 + -4.777777778x + x2 = 7.484567902 Factor a perfect square on the left side: (x + -2.388888889)(x + -2.388888889) = 7.484567902 Calculate the square root of the right side: 2.735793834 Break this problem into two subproblems by setting (x + -2.388888889) equal to 2.735793834 and -2.735793834.Subproblem 1
x + -2.388888889 = 2.735793834 Simplifying x + -2.388888889 = 2.735793834 Reorder the terms: -2.388888889 + x = 2.735793834 Solving -2.388888889 + x = 2.735793834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.388888889' to each side of the equation. -2.388888889 + 2.388888889 + x = 2.735793834 + 2.388888889 Combine like terms: -2.388888889 + 2.388888889 = 0.000000000 0.000000000 + x = 2.735793834 + 2.388888889 x = 2.735793834 + 2.388888889 Combine like terms: 2.735793834 + 2.388888889 = 5.124682723 x = 5.124682723 Simplifying x = 5.124682723Subproblem 2
x + -2.388888889 = -2.735793834 Simplifying x + -2.388888889 = -2.735793834 Reorder the terms: -2.388888889 + x = -2.735793834 Solving -2.388888889 + x = -2.735793834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.388888889' to each side of the equation. -2.388888889 + 2.388888889 + x = -2.735793834 + 2.388888889 Combine like terms: -2.388888889 + 2.388888889 = 0.000000000 0.000000000 + x = -2.735793834 + 2.388888889 x = -2.735793834 + 2.388888889 Combine like terms: -2.735793834 + 2.388888889 = -0.346904945 x = -0.346904945 Simplifying x = -0.346904945Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.124682723, -0.346904945}Solution
x = {5.124682723, -0.346904945}
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