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Simplifying 7x2 + 3x + -42 = 0 Reorder the terms: -42 + 3x + 7x2 = 0 Solving -42 + 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 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 0.4285714286x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 0.4285714286x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 0.4285714286x + x2 = 0 + 6 0.4285714286x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 0.4285714286x + x2 = 6 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 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 6 + 0.04591836735 Combine like terms: 6 + 0.04591836735 = 6.04591836735 0.04591836735 + 0.4285714286x + x2 = 6.04591836735 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 6.04591836735 Calculate the square root of the right side: 2.458844925 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 2.458844925 and -2.458844925.Subproblem 1
x + 0.2142857143 = 2.458844925 Simplifying x + 0.2142857143 = 2.458844925 Reorder the terms: 0.2142857143 + x = 2.458844925 Solving 0.2142857143 + x = 2.458844925 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 = 2.458844925 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 2.458844925 + -0.2142857143 x = 2.458844925 + -0.2142857143 Combine like terms: 2.458844925 + -0.2142857143 = 2.2445592107 x = 2.2445592107 Simplifying x = 2.2445592107Subproblem 2
x + 0.2142857143 = -2.458844925 Simplifying x + 0.2142857143 = -2.458844925 Reorder the terms: 0.2142857143 + x = -2.458844925 Solving 0.2142857143 + x = -2.458844925 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 = -2.458844925 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -2.458844925 + -0.2142857143 x = -2.458844925 + -0.2142857143 Combine like terms: -2.458844925 + -0.2142857143 = -2.6731306393 x = -2.6731306393 Simplifying x = -2.6731306393Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2445592107, -2.6731306393}
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