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Simplifying 4x2 + -84x + 40 = 0 Reorder the terms: 40 + -84x + 4x2 = 0 Solving 40 + -84x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(10 + -21x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(10 + -21x + x2)' equal to zero and attempt to solve: Simplifying 10 + -21x + x2 = 0 Solving 10 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -21x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -21x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -21x + x2 = 0 + -10 -21x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -21x + x2 = -10 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 = -10 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -10 + 110.25 Combine like terms: -10 + 110.25 = 100.25 110.25 + -21x + x2 = 100.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + -10.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + -10.5 = 10.012492197 Simplifying x + -10.5 = 10.012492197 Reorder the terms: -10.5 + x = 10.012492197 Solving -10.5 + x = 10.012492197 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 = 10.012492197 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 10.012492197 + 10.5 x = 10.012492197 + 10.5 Combine like terms: 10.012492197 + 10.5 = 20.512492197 x = 20.512492197 Simplifying x = 20.512492197Subproblem 2
x + -10.5 = -10.012492197 Simplifying x + -10.5 = -10.012492197 Reorder the terms: -10.5 + x = -10.012492197 Solving -10.5 + x = -10.012492197 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 = -10.012492197 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -10.012492197 + 10.5 x = -10.012492197 + 10.5 Combine like terms: -10.012492197 + 10.5 = 0.487507803 x = 0.487507803 Simplifying x = 0.487507803Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.512492197, 0.487507803}Solution
x = {20.512492197, 0.487507803}
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