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Simplifying 4x2 + -40x + 78 = 0 Reorder the terms: 78 + -40x + 4x2 = 0 Solving 78 + -40x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(39 + -20x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(39 + -20x + 2x2)' equal to zero and attempt to solve: Simplifying 39 + -20x + 2x2 = 0 Solving 39 + -20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 19.5 + -10x + x2 = 0 Move the constant term to the right: Add '-19.5' to each side of the equation. 19.5 + -10x + -19.5 + x2 = 0 + -19.5 Reorder the terms: 19.5 + -19.5 + -10x + x2 = 0 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + -10x + x2 = 0 + -19.5 -10x + x2 = 0 + -19.5 Combine like terms: 0 + -19.5 = -19.5 -10x + x2 = -19.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -19.5 + 25 Reorder the terms: 25 + -10x + x2 = -19.5 + 25 Combine like terms: -19.5 + 25 = 5.5 25 + -10x + x2 = 5.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (x + -5) equal to 2.34520788 and -2.34520788.Subproblem 1
x + -5 = 2.34520788 Simplifying x + -5 = 2.34520788 Reorder the terms: -5 + x = 2.34520788 Solving -5 + x = 2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.34520788 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.34520788 + 5 x = 2.34520788 + 5 Combine like terms: 2.34520788 + 5 = 7.34520788 x = 7.34520788 Simplifying x = 7.34520788Subproblem 2
x + -5 = -2.34520788 Simplifying x + -5 = -2.34520788 Reorder the terms: -5 + x = -2.34520788 Solving -5 + x = -2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.34520788 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.34520788 + 5 x = -2.34520788 + 5 Combine like terms: -2.34520788 + 5 = 2.65479212 x = 2.65479212 Simplifying x = 2.65479212Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.34520788, 2.65479212}Solution
x = {7.34520788, 2.65479212}
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