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Simplifying 7x2 + -4x + -32 = 0 Reorder the terms: -32 + -4x + 7x2 = 0 Solving -32 + -4x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.571428571 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '4.571428571' to each side of the equation. -4.571428571 + -0.5714285714x + 4.571428571 + x2 = 0 + 4.571428571 Reorder the terms: -4.571428571 + 4.571428571 + -0.5714285714x + x2 = 0 + 4.571428571 Combine like terms: -4.571428571 + 4.571428571 = 0.000000000 0.000000000 + -0.5714285714x + x2 = 0 + 4.571428571 -0.5714285714x + x2 = 0 + 4.571428571 Combine like terms: 0 + 4.571428571 = 4.571428571 -0.5714285714x + x2 = 4.571428571 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 = 4.571428571 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 4.571428571 + 0.08163265305 Combine like terms: 4.571428571 + 0.08163265305 = 4.65306122405 0.08163265305 + -0.5714285714x + x2 = 4.65306122405 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 4.65306122405 Calculate the square root of the right side: 2.157095553 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 2.157095553 and -2.157095553.Subproblem 1
x + -0.2857142857 = 2.157095553 Simplifying x + -0.2857142857 = 2.157095553 Reorder the terms: -0.2857142857 + x = 2.157095553 Solving -0.2857142857 + x = 2.157095553 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 = 2.157095553 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 2.157095553 + 0.2857142857 x = 2.157095553 + 0.2857142857 Combine like terms: 2.157095553 + 0.2857142857 = 2.4428098387 x = 2.4428098387 Simplifying x = 2.4428098387Subproblem 2
x + -0.2857142857 = -2.157095553 Simplifying x + -0.2857142857 = -2.157095553 Reorder the terms: -0.2857142857 + x = -2.157095553 Solving -0.2857142857 + x = -2.157095553 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 = -2.157095553 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -2.157095553 + 0.2857142857 x = -2.157095553 + 0.2857142857 Combine like terms: -2.157095553 + 0.2857142857 = -1.8713812673 x = -1.8713812673 Simplifying x = -1.8713812673Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4428098387, -1.8713812673}
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