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Simplifying 0 = 4x2 + 35x + -84 Reorder the terms: 0 = -84 + 35x + 4x2 Solving 0 = -84 + 35x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 84 = 84 84 + -35x + -4x2 = -84 + 35x + 4x2 + 84 + -35x + -4x2 Reorder the terms: 84 + -35x + -4x2 = -84 + 84 + 35x + -35x + 4x2 + -4x2 Combine like terms: -84 + 84 = 0 84 + -35x + -4x2 = 0 + 35x + -35x + 4x2 + -4x2 84 + -35x + -4x2 = 35x + -35x + 4x2 + -4x2 Combine like terms: 35x + -35x = 0 84 + -35x + -4x2 = 0 + 4x2 + -4x2 84 + -35x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 84 + -35x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -21 + 8.75x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 8.75x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 8.75x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 8.75x + x2 = 0 + 21 8.75x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 8.75x + x2 = 21 The x term is 8.75x. Take half its coefficient (4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. 8.75x + 19.140625 + x2 = 21 + 19.140625 Reorder the terms: 19.140625 + 8.75x + x2 = 21 + 19.140625 Combine like terms: 21 + 19.140625 = 40.140625 19.140625 + 8.75x + x2 = 40.140625 Factor a perfect square on the left side: (x + 4.375)(x + 4.375) = 40.140625 Calculate the square root of the right side: 6.335662949 Break this problem into two subproblems by setting (x + 4.375) equal to 6.335662949 and -6.335662949.Subproblem 1
x + 4.375 = 6.335662949 Simplifying x + 4.375 = 6.335662949 Reorder the terms: 4.375 + x = 6.335662949 Solving 4.375 + x = 6.335662949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = 6.335662949 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = 6.335662949 + -4.375 x = 6.335662949 + -4.375 Combine like terms: 6.335662949 + -4.375 = 1.960662949 x = 1.960662949 Simplifying x = 1.960662949Subproblem 2
x + 4.375 = -6.335662949 Simplifying x + 4.375 = -6.335662949 Reorder the terms: 4.375 + x = -6.335662949 Solving 4.375 + x = -6.335662949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = -6.335662949 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = -6.335662949 + -4.375 x = -6.335662949 + -4.375 Combine like terms: -6.335662949 + -4.375 = -10.710662949 x = -10.710662949 Simplifying x = -10.710662949Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.960662949, -10.710662949}
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