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Simplifying 7x2 + 12x + -1 = 0 Reorder the terms: -1 + 12x + 7x2 = 0 Solving -1 + 12x + 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'. -0.1428571429 + 1.714285714x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 1.714285714x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 1.714285714x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 1.714285714x + x2 = 0 + 0.1428571429 1.714285714x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 1.714285714x + x2 = 0.1428571429 The x term is 1.714285714x. Take half its coefficient (0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. 1.714285714x + 0.7346938773 + x2 = 0.1428571429 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714x + x2 = 0.1428571429 + 0.7346938773 Combine like terms: 0.1428571429 + 0.7346938773 = 0.8775510202 0.7346938773 + 1.714285714x + x2 = 0.8775510202 Factor a perfect square on the left side: (x + 0.857142857)(x + 0.857142857) = 0.8775510202 Calculate the square root of the right side: 0.936776932 Break this problem into two subproblems by setting (x + 0.857142857) equal to 0.936776932 and -0.936776932.Subproblem 1
x + 0.857142857 = 0.936776932 Simplifying x + 0.857142857 = 0.936776932 Reorder the terms: 0.857142857 + x = 0.936776932 Solving 0.857142857 + x = 0.936776932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = 0.936776932 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = 0.936776932 + -0.857142857 x = 0.936776932 + -0.857142857 Combine like terms: 0.936776932 + -0.857142857 = 0.079634075 x = 0.079634075 Simplifying x = 0.079634075Subproblem 2
x + 0.857142857 = -0.936776932 Simplifying x + 0.857142857 = -0.936776932 Reorder the terms: 0.857142857 + x = -0.936776932 Solving 0.857142857 + x = -0.936776932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + x = -0.936776932 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + x = -0.936776932 + -0.857142857 x = -0.936776932 + -0.857142857 Combine like terms: -0.936776932 + -0.857142857 = -1.793919789 x = -1.793919789 Simplifying x = -1.793919789Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.079634075, -1.793919789}
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