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Simplifying 4x2 + -28x + 7 = 0 Reorder the terms: 7 + -28x + 4x2 = 0 Solving 7 + -28x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -7x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -7x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -7x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -7x + x2 = 0 + -1.75 -7x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -7x + x2 = -1.75 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -1.75 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -1.75 + 12.25 Combine like terms: -1.75 + 12.25 = 10.5 12.25 + -7x + x2 = 10.5 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (x + -3.5) equal to 3.240370349 and -3.240370349.Subproblem 1
x + -3.5 = 3.240370349 Simplifying x + -3.5 = 3.240370349 Reorder the terms: -3.5 + x = 3.240370349 Solving -3.5 + x = 3.240370349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.240370349 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.240370349 + 3.5 x = 3.240370349 + 3.5 Combine like terms: 3.240370349 + 3.5 = 6.740370349 x = 6.740370349 Simplifying x = 6.740370349Subproblem 2
x + -3.5 = -3.240370349 Simplifying x + -3.5 = -3.240370349 Reorder the terms: -3.5 + x = -3.240370349 Solving -3.5 + x = -3.240370349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.240370349 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.240370349 + 3.5 x = -3.240370349 + 3.5 Combine like terms: -3.240370349 + 3.5 = 0.259629651 x = 0.259629651 Simplifying x = 0.259629651Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.740370349, 0.259629651}
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