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Simplifying (7x + 4) * 2x + -16 = 1 Reorder the terms: (4 + 7x) * 2x + -16 = 1 Reorder the terms for easier multiplication: 2x(4 + 7x) + -16 = 1 (4 * 2x + 7x * 2x) + -16 = 1 (8x + 14x2) + -16 = 1 Reorder the terms: -16 + 8x + 14x2 = 1 Solving -16 + 8x + 14x2 = 1 Solving for variable 'x'. Reorder the terms: -16 + -1 + 8x + 14x2 = 1 + -1 Combine like terms: -16 + -1 = -17 -17 + 8x + 14x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -17 + 8x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.214285714 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '1.214285714' to each side of the equation. -1.214285714 + 0.5714285714x + 1.214285714 + x2 = 0 + 1.214285714 Reorder the terms: -1.214285714 + 1.214285714 + 0.5714285714x + x2 = 0 + 1.214285714 Combine like terms: -1.214285714 + 1.214285714 = 0.000000000 0.000000000 + 0.5714285714x + x2 = 0 + 1.214285714 0.5714285714x + x2 = 0 + 1.214285714 Combine like terms: 0 + 1.214285714 = 1.214285714 0.5714285714x + x2 = 1.214285714 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 1.214285714 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 1.214285714 + 0.08163265305 Combine like terms: 1.214285714 + 0.08163265305 = 1.29591836705 0.08163265305 + 0.5714285714x + x2 = 1.29591836705 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 1.29591836705 Calculate the square root of the right side: 1.138384103 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 1.138384103 and -1.138384103.Subproblem 1
x + 0.2857142857 = 1.138384103 Simplifying x + 0.2857142857 = 1.138384103 Reorder the terms: 0.2857142857 + x = 1.138384103 Solving 0.2857142857 + x = 1.138384103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 1.138384103 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 1.138384103 + -0.2857142857 x = 1.138384103 + -0.2857142857 Combine like terms: 1.138384103 + -0.2857142857 = 0.8526698173 x = 0.8526698173 Simplifying x = 0.8526698173Subproblem 2
x + 0.2857142857 = -1.138384103 Simplifying x + 0.2857142857 = -1.138384103 Reorder the terms: 0.2857142857 + x = -1.138384103 Solving 0.2857142857 + x = -1.138384103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -1.138384103 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -1.138384103 + -0.2857142857 x = -1.138384103 + -0.2857142857 Combine like terms: -1.138384103 + -0.2857142857 = -1.4240983887 x = -1.4240983887 Simplifying x = -1.4240983887Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8526698173, -1.4240983887}
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