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Simplifying 4x2 + -40x + 97 = 0 Reorder the terms: 97 + -40x + 4x2 = 0 Solving 97 + -40x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 24.25 + -10x + x2 = 0 Move the constant term to the right: Add '-24.25' to each side of the equation. 24.25 + -10x + -24.25 + x2 = 0 + -24.25 Reorder the terms: 24.25 + -24.25 + -10x + x2 = 0 + -24.25 Combine like terms: 24.25 + -24.25 = 0.00 0.00 + -10x + x2 = 0 + -24.25 -10x + x2 = 0 + -24.25 Combine like terms: 0 + -24.25 = -24.25 -10x + x2 = -24.25 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 = -24.25 + 25 Reorder the terms: 25 + -10x + x2 = -24.25 + 25 Combine like terms: -24.25 + 25 = 0.75 25 + -10x + x2 = 0.75 Factor a perfect square on the left side: (x + -5)(x + -5) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x + -5) equal to 0.866025404 and -0.866025404.Subproblem 1
x + -5 = 0.866025404 Simplifying x + -5 = 0.866025404 Reorder the terms: -5 + x = 0.866025404 Solving -5 + x = 0.866025404 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 = 0.866025404 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0.866025404 + 5 x = 0.866025404 + 5 Combine like terms: 0.866025404 + 5 = 5.866025404 x = 5.866025404 Simplifying x = 5.866025404Subproblem 2
x + -5 = -0.866025404 Simplifying x + -5 = -0.866025404 Reorder the terms: -5 + x = -0.866025404 Solving -5 + x = -0.866025404 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 = -0.866025404 + 5 Combine like terms: -5 + 5 = 0 0 + x = -0.866025404 + 5 x = -0.866025404 + 5 Combine like terms: -0.866025404 + 5 = 4.133974596 x = 4.133974596 Simplifying x = 4.133974596Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.866025404, 4.133974596}
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