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Simplifying 2x2 + 4x + -69 = 0 Reorder the terms: -69 + 4x + 2x2 = 0 Solving -69 + 4x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -34.5 + 2x + x2 = 0 Move the constant term to the right: Add '34.5' to each side of the equation. -34.5 + 2x + 34.5 + x2 = 0 + 34.5 Reorder the terms: -34.5 + 34.5 + 2x + x2 = 0 + 34.5 Combine like terms: -34.5 + 34.5 = 0.0 0.0 + 2x + x2 = 0 + 34.5 2x + x2 = 0 + 34.5 Combine like terms: 0 + 34.5 = 34.5 2x + x2 = 34.5 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 = 34.5 + 1 Reorder the terms: 1 + 2x + x2 = 34.5 + 1 Combine like terms: 34.5 + 1 = 35.5 1 + 2x + x2 = 35.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 35.5 Calculate the square root of the right side: 5.958187644 Break this problem into two subproblems by setting (x + 1) equal to 5.958187644 and -5.958187644.Subproblem 1
x + 1 = 5.958187644 Simplifying x + 1 = 5.958187644 Reorder the terms: 1 + x = 5.958187644 Solving 1 + x = 5.958187644 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 = 5.958187644 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.958187644 + -1 x = 5.958187644 + -1 Combine like terms: 5.958187644 + -1 = 4.958187644 x = 4.958187644 Simplifying x = 4.958187644Subproblem 2
x + 1 = -5.958187644 Simplifying x + 1 = -5.958187644 Reorder the terms: 1 + x = -5.958187644 Solving 1 + x = -5.958187644 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 = -5.958187644 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.958187644 + -1 x = -5.958187644 + -1 Combine like terms: -5.958187644 + -1 = -6.958187644 x = -6.958187644 Simplifying x = -6.958187644Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.958187644, -6.958187644}
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