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Simplifying 4x2 + 8x + -35 = 0 Reorder the terms: -35 + 8x + 4x2 = 0 Solving -35 + 8x + 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 + 2x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 2x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 2x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 2x + x2 = 0 + 8.75 2x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 2x + x2 = 8.75 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 8.75 + 1 Reorder the terms: 1 + 2x + x2 = 8.75 + 1 Combine like terms: 8.75 + 1 = 9.75 1 + 2x + x2 = 9.75 Factor a perfect square on the left side: (x + 1)(x + 1) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (x + 1) equal to 3.122498999 and -3.122498999.Subproblem 1
x + 1 = 3.122498999 Simplifying x + 1 = 3.122498999 Reorder the terms: 1 + x = 3.122498999 Solving 1 + x = 3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.122498999 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.122498999 + -1 x = 3.122498999 + -1 Combine like terms: 3.122498999 + -1 = 2.122498999 x = 2.122498999 Simplifying x = 2.122498999Subproblem 2
x + 1 = -3.122498999 Simplifying x + 1 = -3.122498999 Reorder the terms: 1 + x = -3.122498999 Solving 1 + x = -3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.122498999 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.122498999 + -1 x = -3.122498999 + -1 Combine like terms: -3.122498999 + -1 = -4.122498999 x = -4.122498999 Simplifying x = -4.122498999Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.122498999, -4.122498999}
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