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Simplifying 42x2 + -69x + 20 = 7x2 Reorder the terms: 20 + -69x + 42x2 = 7x2 Solving 20 + -69x + 42x2 = 7x2 Solving for variable 'x'. Combine like terms: 42x2 + -7x2 = 35x2 20 + -69x + 35x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 20 + -69x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.5714285714 + -1.971428571x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -1.971428571x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -1.971428571x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -1.971428571x + x2 = 0 + -0.5714285714 -1.971428571x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -1.971428571x + x2 = -0.5714285714 The x term is -1.971428571x. Take half its coefficient (-0.9857142855). Square it (0.9716326526) and add it to both sides. Add '0.9716326526' to each side of the equation. -1.971428571x + 0.9716326526 + x2 = -0.5714285714 + 0.9716326526 Reorder the terms: 0.9716326526 + -1.971428571x + x2 = -0.5714285714 + 0.9716326526 Combine like terms: -0.5714285714 + 0.9716326526 = 0.4002040812 0.9716326526 + -1.971428571x + x2 = 0.4002040812 Factor a perfect square on the left side: (x + -0.9857142855)(x + -0.9857142855) = 0.4002040812 Calculate the square root of the right side: 0.632616852 Break this problem into two subproblems by setting (x + -0.9857142855) equal to 0.632616852 and -0.632616852.Subproblem 1
x + -0.9857142855 = 0.632616852 Simplifying x + -0.9857142855 = 0.632616852 Reorder the terms: -0.9857142855 + x = 0.632616852 Solving -0.9857142855 + x = 0.632616852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9857142855' to each side of the equation. -0.9857142855 + 0.9857142855 + x = 0.632616852 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + x = 0.632616852 + 0.9857142855 x = 0.632616852 + 0.9857142855 Combine like terms: 0.632616852 + 0.9857142855 = 1.6183311375 x = 1.6183311375 Simplifying x = 1.6183311375Subproblem 2
x + -0.9857142855 = -0.632616852 Simplifying x + -0.9857142855 = -0.632616852 Reorder the terms: -0.9857142855 + x = -0.632616852 Solving -0.9857142855 + x = -0.632616852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9857142855' to each side of the equation. -0.9857142855 + 0.9857142855 + x = -0.632616852 + 0.9857142855 Combine like terms: -0.9857142855 + 0.9857142855 = 0.0000000000 0.0000000000 + x = -0.632616852 + 0.9857142855 x = -0.632616852 + 0.9857142855 Combine like terms: -0.632616852 + 0.9857142855 = 0.3530974335 x = 0.3530974335 Simplifying x = 0.3530974335Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6183311375, 0.3530974335}
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