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Simplifying 4x2 + 8x + -13 = 0 Reorder the terms: -13 + 8x + 4x2 = 0 Solving -13 + 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'. -3.25 + 2x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 2x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 2x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 2x + x2 = 0 + 3.25 2x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 2x + x2 = 3.25 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 = 3.25 + 1 Reorder the terms: 1 + 2x + x2 = 3.25 + 1 Combine like terms: 3.25 + 1 = 4.25 1 + 2x + x2 = 4.25 Factor a perfect square on the left side: (x + 1)(x + 1) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 1) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 1 = 2.061552813 Simplifying x + 1 = 2.061552813 Reorder the terms: 1 + x = 2.061552813 Solving 1 + x = 2.061552813 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 = 2.061552813 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.061552813 + -1 x = 2.061552813 + -1 Combine like terms: 2.061552813 + -1 = 1.061552813 x = 1.061552813 Simplifying x = 1.061552813Subproblem 2
x + 1 = -2.061552813 Simplifying x + 1 = -2.061552813 Reorder the terms: 1 + x = -2.061552813 Solving 1 + x = -2.061552813 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 = -2.061552813 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.061552813 + -1 x = -2.061552813 + -1 Combine like terms: -2.061552813 + -1 = -3.061552813 x = -3.061552813 Simplifying x = -3.061552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.061552813, -3.061552813}
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