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Simplifying -7x2 + 3x + 46 = 0 Reorder the terms: 46 + 3x + -7x2 = 0 Solving 46 + 3x + -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'. -6.571428571 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '6.571428571' to each side of the equation. -6.571428571 + -0.4285714286x + 6.571428571 + x2 = 0 + 6.571428571 Reorder the terms: -6.571428571 + 6.571428571 + -0.4285714286x + x2 = 0 + 6.571428571 Combine like terms: -6.571428571 + 6.571428571 = 0.000000000 0.000000000 + -0.4285714286x + x2 = 0 + 6.571428571 -0.4285714286x + x2 = 0 + 6.571428571 Combine like terms: 0 + 6.571428571 = 6.571428571 -0.4285714286x + x2 = 6.571428571 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 = 6.571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 6.571428571 + 0.04591836735 Combine like terms: 6.571428571 + 0.04591836735 = 6.61734693835 0.04591836735 + -0.4285714286x + x2 = 6.61734693835 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 6.61734693835 Calculate the square root of the right side: 2.572420444 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 2.572420444 and -2.572420444.Subproblem 1
x + -0.2142857143 = 2.572420444 Simplifying x + -0.2142857143 = 2.572420444 Reorder the terms: -0.2142857143 + x = 2.572420444 Solving -0.2142857143 + x = 2.572420444 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 = 2.572420444 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 2.572420444 + 0.2142857143 x = 2.572420444 + 0.2142857143 Combine like terms: 2.572420444 + 0.2142857143 = 2.7867061583 x = 2.7867061583 Simplifying x = 2.7867061583Subproblem 2
x + -0.2142857143 = -2.572420444 Simplifying x + -0.2142857143 = -2.572420444 Reorder the terms: -0.2142857143 + x = -2.572420444 Solving -0.2142857143 + x = -2.572420444 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 = -2.572420444 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -2.572420444 + 0.2142857143 x = -2.572420444 + 0.2142857143 Combine like terms: -2.572420444 + 0.2142857143 = -2.3581347297 x = -2.3581347297 Simplifying x = -2.3581347297Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7867061583, -2.3581347297}
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