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Simplifying 5x + -1(x + -3) + 2 = 7(2x + 1)(x + 4) + -19 Reorder the terms: 5x + -1(-3 + x) + 2 = 7(2x + 1)(x + 4) + -19 5x + (-3 * -1 + x * -1) + 2 = 7(2x + 1)(x + 4) + -19 5x + (3 + -1x) + 2 = 7(2x + 1)(x + 4) + -19 Reorder the terms: 3 + 2 + 5x + -1x = 7(2x + 1)(x + 4) + -19 Combine like terms: 3 + 2 = 5 5 + 5x + -1x = 7(2x + 1)(x + 4) + -19 Combine like terms: 5x + -1x = 4x 5 + 4x = 7(2x + 1)(x + 4) + -19 Reorder the terms: 5 + 4x = 7(1 + 2x)(x + 4) + -19 Reorder the terms: 5 + 4x = 7(1 + 2x)(4 + x) + -19 Multiply (1 + 2x) * (4 + x) 5 + 4x = 7(1(4 + x) + 2x * (4 + x)) + -19 5 + 4x = 7((4 * 1 + x * 1) + 2x * (4 + x)) + -19 5 + 4x = 7((4 + 1x) + 2x * (4 + x)) + -19 5 + 4x = 7(4 + 1x + (4 * 2x + x * 2x)) + -19 5 + 4x = 7(4 + 1x + (8x + 2x2)) + -19 Combine like terms: 1x + 8x = 9x 5 + 4x = 7(4 + 9x + 2x2) + -19 5 + 4x = (4 * 7 + 9x * 7 + 2x2 * 7) + -19 5 + 4x = (28 + 63x + 14x2) + -19 Reorder the terms: 5 + 4x = 28 + -19 + 63x + 14x2 Combine like terms: 28 + -19 = 9 5 + 4x = 9 + 63x + 14x2 Solving 5 + 4x = 9 + 63x + 14x2 Solving for variable 'x'. Reorder the terms: 5 + -9 + 4x + -63x + -14x2 = 9 + 63x + 14x2 + -9 + -63x + -14x2 Combine like terms: 5 + -9 = -4 -4 + 4x + -63x + -14x2 = 9 + 63x + 14x2 + -9 + -63x + -14x2 Combine like terms: 4x + -63x = -59x -4 + -59x + -14x2 = 9 + 63x + 14x2 + -9 + -63x + -14x2 Reorder the terms: -4 + -59x + -14x2 = 9 + -9 + 63x + -63x + 14x2 + -14x2 Combine like terms: 9 + -9 = 0 -4 + -59x + -14x2 = 0 + 63x + -63x + 14x2 + -14x2 -4 + -59x + -14x2 = 63x + -63x + 14x2 + -14x2 Combine like terms: 63x + -63x = 0 -4 + -59x + -14x2 = 0 + 14x2 + -14x2 -4 + -59x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -4 + -59x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 59x + 14x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 59x + 14x2)' equal to zero and attempt to solve: Simplifying 4 + 59x + 14x2 = 0 Solving 4 + 59x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.2857142857 + 4.214285714x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 4.214285714x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 4.214285714x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 4.214285714x + x2 = 0 + -0.2857142857 4.214285714x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 4.214285714x + x2 = -0.2857142857 The x term is 4.214285714x. Take half its coefficient (2.107142857). Square it (4.440051020) and add it to both sides. Add '4.440051020' to each side of the equation. 4.214285714x + 4.440051020 + x2 = -0.2857142857 + 4.440051020 Reorder the terms: 4.440051020 + 4.214285714x + x2 = -0.2857142857 + 4.440051020 Combine like terms: -0.2857142857 + 4.440051020 = 4.1543367343 4.440051020 + 4.214285714x + x2 = 4.1543367343 Factor a perfect square on the left side: (x + 2.107142857)(x + 2.107142857) = 4.1543367343 Calculate the square root of the right side: 2.03821901 Break this problem into two subproblems by setting (x + 2.107142857) equal to 2.03821901 and -2.03821901.Subproblem 1
x + 2.107142857 = 2.03821901 Simplifying x + 2.107142857 = 2.03821901 Reorder the terms: 2.107142857 + x = 2.03821901 Solving 2.107142857 + x = 2.03821901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.107142857' to each side of the equation. 2.107142857 + -2.107142857 + x = 2.03821901 + -2.107142857 Combine like terms: 2.107142857 + -2.107142857 = 0.000000000 0.000000000 + x = 2.03821901 + -2.107142857 x = 2.03821901 + -2.107142857 Combine like terms: 2.03821901 + -2.107142857 = -0.068923847 x = -0.068923847 Simplifying x = -0.068923847Subproblem 2
x + 2.107142857 = -2.03821901 Simplifying x + 2.107142857 = -2.03821901 Reorder the terms: 2.107142857 + x = -2.03821901 Solving 2.107142857 + x = -2.03821901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.107142857' to each side of the equation. 2.107142857 + -2.107142857 + x = -2.03821901 + -2.107142857 Combine like terms: 2.107142857 + -2.107142857 = 0.000000000 0.000000000 + x = -2.03821901 + -2.107142857 x = -2.03821901 + -2.107142857 Combine like terms: -2.03821901 + -2.107142857 = -4.145361867 x = -4.145361867 Simplifying x = -4.145361867Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.068923847, -4.145361867}Solution
x = {-0.068923847, -4.145361867}
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