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Simplifying 78 = 3x2 + 21x Reorder the terms: 78 = 21x + 3x2 Solving 78 = 21x + 3x2 Solving for variable 'x'. Reorder the terms: 78 + -21x + -3x2 = 21x + -21x + 3x2 + -3x2 Combine like terms: 21x + -21x = 0 78 + -21x + -3x2 = 0 + 3x2 + -3x2 78 + -21x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 78 + -21x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(26 + -7x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(26 + -7x + -1x2)' equal to zero and attempt to solve: Simplifying 26 + -7x + -1x2 = 0 Solving 26 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -26 + 7x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + 7x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 7x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 7x + x2 = 0 + 26 7x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 7x + x2 = 26 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 = 26 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 26 + 12.25 Combine like terms: 26 + 12.25 = 38.25 12.25 + 7x + x2 = 38.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + 3.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + 3.5 = 6.184658438 Simplifying x + 3.5 = 6.184658438 Reorder the terms: 3.5 + x = 6.184658438 Solving 3.5 + x = 6.184658438 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 = 6.184658438 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.184658438 + -3.5 x = 6.184658438 + -3.5 Combine like terms: 6.184658438 + -3.5 = 2.684658438 x = 2.684658438 Simplifying x = 2.684658438Subproblem 2
x + 3.5 = -6.184658438 Simplifying x + 3.5 = -6.184658438 Reorder the terms: 3.5 + x = -6.184658438 Solving 3.5 + x = -6.184658438 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 = -6.184658438 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.184658438 + -3.5 x = -6.184658438 + -3.5 Combine like terms: -6.184658438 + -3.5 = -9.684658438 x = -9.684658438 Simplifying x = -9.684658438Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.684658438, -9.684658438}Solution
x = {2.684658438, -9.684658438}
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