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Simplifying 4x2 + -56x + 84 = 0 Reorder the terms: 84 + -56x + 4x2 = 0 Solving 84 + -56x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(21 + -14x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(21 + -14x + x2)' equal to zero and attempt to solve: Simplifying 21 + -14x + x2 = 0 Solving 21 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -14x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -14x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -14x + x2 = 0 + -21 -14x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -14x + x2 = -21 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -21 + 49 Reorder the terms: 49 + -14x + x2 = -21 + 49 Combine like terms: -21 + 49 = 28 49 + -14x + x2 = 28 Factor a perfect square on the left side: (x + -7)(x + -7) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -7) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -7 = 5.291502622 Simplifying x + -7 = 5.291502622 Reorder the terms: -7 + x = 5.291502622 Solving -7 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 5.291502622 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.291502622 + 7 x = 5.291502622 + 7 Combine like terms: 5.291502622 + 7 = 12.291502622 x = 12.291502622 Simplifying x = 12.291502622Subproblem 2
x + -7 = -5.291502622 Simplifying x + -7 = -5.291502622 Reorder the terms: -7 + x = -5.291502622 Solving -7 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -5.291502622 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.291502622 + 7 x = -5.291502622 + 7 Combine like terms: -5.291502622 + 7 = 1.708497378 x = 1.708497378 Simplifying x = 1.708497378Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.291502622, 1.708497378}Solution
x = {12.291502622, 1.708497378}
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