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Simplifying 4x2 + -84x + 140 = 0 Reorder the terms: 140 + -84x + 4x2 = 0 Solving 140 + -84x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(35 + -21x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(35 + -21x + x2)' equal to zero and attempt to solve: Simplifying 35 + -21x + x2 = 0 Solving 35 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + -21x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + -21x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -21x + x2 = 0 + -35 -21x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 -21x + x2 = -35 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -35 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -35 + 110.25 Combine like terms: -35 + 110.25 = 75.25 110.25 + -21x + x2 = 75.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 75.25 Calculate the square root of the right side: 8.674675786 Break this problem into two subproblems by setting (x + -10.5) equal to 8.674675786 and -8.674675786.Subproblem 1
x + -10.5 = 8.674675786 Simplifying x + -10.5 = 8.674675786 Reorder the terms: -10.5 + x = 8.674675786 Solving -10.5 + x = 8.674675786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 8.674675786 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 8.674675786 + 10.5 x = 8.674675786 + 10.5 Combine like terms: 8.674675786 + 10.5 = 19.174675786 x = 19.174675786 Simplifying x = 19.174675786Subproblem 2
x + -10.5 = -8.674675786 Simplifying x + -10.5 = -8.674675786 Reorder the terms: -10.5 + x = -8.674675786 Solving -10.5 + x = -8.674675786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -8.674675786 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -8.674675786 + 10.5 x = -8.674675786 + 10.5 Combine like terms: -8.674675786 + 10.5 = 1.825324214 x = 1.825324214 Simplifying x = 1.825324214Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.174675786, 1.825324214}Solution
x = {19.174675786, 1.825324214}
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