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Simplifying 7x2 + -42x + 6 = 0 Reorder the terms: 6 + -42x + 7x2 = 0 Solving 6 + -42x + 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'. 0.8571428571 + -6x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + -6x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + -6x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + -6x + x2 = 0 + -0.8571428571 -6x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 -6x + x2 = -0.8571428571 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -0.8571428571 + 9 Reorder the terms: 9 + -6x + x2 = -0.8571428571 + 9 Combine like terms: -0.8571428571 + 9 = 8.1428571429 9 + -6x + x2 = 8.1428571429 Factor a perfect square on the left side: (x + -3)(x + -3) = 8.1428571429 Calculate the square root of the right side: 2.853569194 Break this problem into two subproblems by setting (x + -3) equal to 2.853569194 and -2.853569194.Subproblem 1
x + -3 = 2.853569194 Simplifying x + -3 = 2.853569194 Reorder the terms: -3 + x = 2.853569194 Solving -3 + x = 2.853569194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.853569194 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.853569194 + 3 x = 2.853569194 + 3 Combine like terms: 2.853569194 + 3 = 5.853569194 x = 5.853569194 Simplifying x = 5.853569194Subproblem 2
x + -3 = -2.853569194 Simplifying x + -3 = -2.853569194 Reorder the terms: -3 + x = -2.853569194 Solving -3 + x = -2.853569194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.853569194 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.853569194 + 3 x = -2.853569194 + 3 Combine like terms: -2.853569194 + 3 = 0.146430806 x = 0.146430806 Simplifying x = 0.146430806Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.853569194, 0.146430806}
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