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Simplifying 7x2 + -1 = 3x Reorder the terms: -1 + 7x2 = 3x Solving -1 + 7x2 = 3x Solving for variable 'x'. Reorder the terms: -1 + -3x + 7x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -1 + -3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.4285714286x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.4285714286x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.4285714286x + x2 = 0 + 0.1428571429 -0.4285714286x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.4285714286x + x2 = 0.1428571429 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = 0.1428571429 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 0.1428571429 + 0.04591836735 Combine like terms: 0.1428571429 + 0.04591836735 = 0.18877551025 0.04591836735 + -0.4285714286x + x2 = 0.18877551025 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 0.18877551025 Calculate the square root of the right side: 0.434483038 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 0.434483038 and -0.434483038.Subproblem 1
x + -0.2142857143 = 0.434483038 Simplifying x + -0.2142857143 = 0.434483038 Reorder the terms: -0.2142857143 + x = 0.434483038 Solving -0.2142857143 + x = 0.434483038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 0.434483038 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 0.434483038 + 0.2142857143 x = 0.434483038 + 0.2142857143 Combine like terms: 0.434483038 + 0.2142857143 = 0.6487687523 x = 0.6487687523 Simplifying x = 0.6487687523Subproblem 2
x + -0.2142857143 = -0.434483038 Simplifying x + -0.2142857143 = -0.434483038 Reorder the terms: -0.2142857143 + x = -0.434483038 Solving -0.2142857143 + x = -0.434483038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -0.434483038 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -0.434483038 + 0.2142857143 x = -0.434483038 + 0.2142857143 Combine like terms: -0.434483038 + 0.2142857143 = -0.2201973237 x = -0.2201973237 Simplifying x = -0.2201973237Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6487687523, -0.2201973237}
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