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Simplifying 4x2 + -16x + -35 = 0 Reorder the terms: -35 + -16x + 4x2 = 0 Solving -35 + -16x + 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'. -8.75 + -4x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -4x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -4x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -4x + x2 = 0 + 8.75 -4x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -4x + x2 = 8.75 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 8.75 + 4 Reorder the terms: 4 + -4x + x2 = 8.75 + 4 Combine like terms: 8.75 + 4 = 12.75 4 + -4x + x2 = 12.75 Factor a perfect square on the left side: (x + -2)(x + -2) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (x + -2) equal to 3.570714214 and -3.570714214.Subproblem 1
x + -2 = 3.570714214 Simplifying x + -2 = 3.570714214 Reorder the terms: -2 + x = 3.570714214 Solving -2 + x = 3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.570714214 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.570714214 + 2 x = 3.570714214 + 2 Combine like terms: 3.570714214 + 2 = 5.570714214 x = 5.570714214 Simplifying x = 5.570714214Subproblem 2
x + -2 = -3.570714214 Simplifying x + -2 = -3.570714214 Reorder the terms: -2 + x = -3.570714214 Solving -2 + x = -3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.570714214 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.570714214 + 2 x = -3.570714214 + 2 Combine like terms: -3.570714214 + 2 = -1.570714214 x = -1.570714214 Simplifying x = -1.570714214Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.570714214, -1.570714214}
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