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Simplifying 28x2 + -12x + -7 = 0 Reorder the terms: -7 + -12x + 28x2 = 0 Solving -7 + -12x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.25 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.4285714286x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.4285714286x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.4285714286x + x2 = 0 + 0.25 -0.4285714286x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.4285714286x + x2 = 0.25 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 = 0.25 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 0.25 + 0.04591836735 Combine like terms: 0.25 + 0.04591836735 = 0.29591836735 0.04591836735 + -0.4285714286x + x2 = 0.29591836735 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 0.29591836735 Calculate the square root of the right side: 0.543983793 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 0.543983793 and -0.543983793.Subproblem 1
x + -0.2142857143 = 0.543983793 Simplifying x + -0.2142857143 = 0.543983793 Reorder the terms: -0.2142857143 + x = 0.543983793 Solving -0.2142857143 + x = 0.543983793 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 = 0.543983793 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 0.543983793 + 0.2142857143 x = 0.543983793 + 0.2142857143 Combine like terms: 0.543983793 + 0.2142857143 = 0.7582695073 x = 0.7582695073 Simplifying x = 0.7582695073Subproblem 2
x + -0.2142857143 = -0.543983793 Simplifying x + -0.2142857143 = -0.543983793 Reorder the terms: -0.2142857143 + x = -0.543983793 Solving -0.2142857143 + x = -0.543983793 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 = -0.543983793 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -0.543983793 + 0.2142857143 x = -0.543983793 + 0.2142857143 Combine like terms: -0.543983793 + 0.2142857143 = -0.3296980787 x = -0.3296980787 Simplifying x = -0.3296980787Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7582695073, -0.3296980787}
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