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Simplifying 4x2 + 140x + 785 = 0 Reorder the terms: 785 + 140x + 4x2 = 0 Solving 785 + 140x + 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'. 196.25 + 35x + x2 = 0 Move the constant term to the right: Add '-196.25' to each side of the equation. 196.25 + 35x + -196.25 + x2 = 0 + -196.25 Reorder the terms: 196.25 + -196.25 + 35x + x2 = 0 + -196.25 Combine like terms: 196.25 + -196.25 = 0.00 0.00 + 35x + x2 = 0 + -196.25 35x + x2 = 0 + -196.25 Combine like terms: 0 + -196.25 = -196.25 35x + x2 = -196.25 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = -196.25 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -196.25 + 306.25 Combine like terms: -196.25 + 306.25 = 110 306.25 + 35x + x2 = 110 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (x + 17.5) equal to 10.488088482 and -10.488088482.Subproblem 1
x + 17.5 = 10.488088482 Simplifying x + 17.5 = 10.488088482 Reorder the terms: 17.5 + x = 10.488088482 Solving 17.5 + x = 10.488088482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 10.488088482 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 10.488088482 + -17.5 x = 10.488088482 + -17.5 Combine like terms: 10.488088482 + -17.5 = -7.011911518 x = -7.011911518 Simplifying x = -7.011911518Subproblem 2
x + 17.5 = -10.488088482 Simplifying x + 17.5 = -10.488088482 Reorder the terms: 17.5 + x = -10.488088482 Solving 17.5 + x = -10.488088482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -10.488088482 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -10.488088482 + -17.5 x = -10.488088482 + -17.5 Combine like terms: -10.488088482 + -17.5 = -27.988088482 x = -27.988088482 Simplifying x = -27.988088482Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.011911518, -27.988088482}
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