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Simplifying 5x(x + -3) + 2 = 7(2x + 4) + -19 Reorder the terms: 5x(-3 + x) + 2 = 7(2x + 4) + -19 (-3 * 5x + x * 5x) + 2 = 7(2x + 4) + -19 (-15x + 5x2) + 2 = 7(2x + 4) + -19 Reorder the terms: 2 + -15x + 5x2 = 7(2x + 4) + -19 Reorder the terms: 2 + -15x + 5x2 = 7(4 + 2x) + -19 2 + -15x + 5x2 = (4 * 7 + 2x * 7) + -19 2 + -15x + 5x2 = (28 + 14x) + -19 Reorder the terms: 2 + -15x + 5x2 = 28 + -19 + 14x Combine like terms: 28 + -19 = 9 2 + -15x + 5x2 = 9 + 14x Solving 2 + -15x + 5x2 = 9 + 14x Solving for variable 'x'. Reorder the terms: 2 + -9 + -15x + -14x + 5x2 = 9 + 14x + -9 + -14x Combine like terms: 2 + -9 = -7 -7 + -15x + -14x + 5x2 = 9 + 14x + -9 + -14x Combine like terms: -15x + -14x = -29x -7 + -29x + 5x2 = 9 + 14x + -9 + -14x Reorder the terms: -7 + -29x + 5x2 = 9 + -9 + 14x + -14x Combine like terms: 9 + -9 = 0 -7 + -29x + 5x2 = 0 + 14x + -14x -7 + -29x + 5x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -7 + -29x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -5.8x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -5.8x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -5.8x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -5.8x + x2 = 0 + 1.4 -5.8x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -5.8x + x2 = 1.4 The x term is -5.8x. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8x + 8.41 + x2 = 1.4 + 8.41 Reorder the terms: 8.41 + -5.8x + x2 = 1.4 + 8.41 Combine like terms: 1.4 + 8.41 = 9.81 8.41 + -5.8x + x2 = 9.81 Factor a perfect square on the left side: (x + -2.9)(x + -2.9) = 9.81 Calculate the square root of the right side: 3.132091953 Break this problem into two subproblems by setting (x + -2.9) equal to 3.132091953 and -3.132091953.Subproblem 1
x + -2.9 = 3.132091953 Simplifying x + -2.9 = 3.132091953 Reorder the terms: -2.9 + x = 3.132091953 Solving -2.9 + x = 3.132091953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = 3.132091953 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = 3.132091953 + 2.9 x = 3.132091953 + 2.9 Combine like terms: 3.132091953 + 2.9 = 6.032091953 x = 6.032091953 Simplifying x = 6.032091953Subproblem 2
x + -2.9 = -3.132091953 Simplifying x + -2.9 = -3.132091953 Reorder the terms: -2.9 + x = -3.132091953 Solving -2.9 + x = -3.132091953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = -3.132091953 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = -3.132091953 + 2.9 x = -3.132091953 + 2.9 Combine like terms: -3.132091953 + 2.9 = -0.232091953 x = -0.232091953 Simplifying x = -0.232091953Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.032091953, -0.232091953}
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