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Simplifying 7x2 + -12x = 1 Reorder the terms: -12x + 7x2 = 1 Solving -12x + 7x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -12x + 7x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -12x + 7x2 = 0 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 = 1.793919789 x = 1.793919789 Simplifying x = 1.793919789Subproblem 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 = -0.079634075 x = -0.079634075 Simplifying x = -0.079634075Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.793919789, -0.079634075}
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