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Simplifying 6 = 4x2 + -28x + 49 Reorder the terms: 6 = 49 + -28x + 4x2 Solving 6 = 49 + -28x + 4x2 Solving for variable 'x'. Combine like terms: 6 + -49 = -43 -43 + 28x + -4x2 = 49 + -28x + 4x2 + -49 + 28x + -4x2 Reorder the terms: -43 + 28x + -4x2 = 49 + -49 + -28x + 28x + 4x2 + -4x2 Combine like terms: 49 + -49 = 0 -43 + 28x + -4x2 = 0 + -28x + 28x + 4x2 + -4x2 -43 + 28x + -4x2 = -28x + 28x + 4x2 + -4x2 Combine like terms: -28x + 28x = 0 -43 + 28x + -4x2 = 0 + 4x2 + -4x2 -43 + 28x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -43 + 28x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 10.75 + -7x + x2 = 0 Move the constant term to the right: Add '-10.75' to each side of the equation. 10.75 + -7x + -10.75 + x2 = 0 + -10.75 Reorder the terms: 10.75 + -10.75 + -7x + x2 = 0 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + -7x + x2 = 0 + -10.75 -7x + x2 = 0 + -10.75 Combine like terms: 0 + -10.75 = -10.75 -7x + x2 = -10.75 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 = -10.75 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -10.75 + 12.25 Combine like terms: -10.75 + 12.25 = 1.5 12.25 + -7x + x2 = 1.5 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + -3.5) equal to 1.224744871 and -1.224744871.Subproblem 1
x + -3.5 = 1.224744871 Simplifying x + -3.5 = 1.224744871 Reorder the terms: -3.5 + x = 1.224744871 Solving -3.5 + x = 1.224744871 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 = 1.224744871 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.224744871 + 3.5 x = 1.224744871 + 3.5 Combine like terms: 1.224744871 + 3.5 = 4.724744871 x = 4.724744871 Simplifying x = 4.724744871Subproblem 2
x + -3.5 = -1.224744871 Simplifying x + -3.5 = -1.224744871 Reorder the terms: -3.5 + x = -1.224744871 Solving -3.5 + x = -1.224744871 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 = -1.224744871 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.224744871 + 3.5 x = -1.224744871 + 3.5 Combine like terms: -1.224744871 + 3.5 = 2.275255129 x = 2.275255129 Simplifying x = 2.275255129Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.724744871, 2.275255129}
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