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Simplifying 2x2 + 6x + -77 = 0 Reorder the terms: -77 + 6x + 2x2 = 0 Solving -77 + 6x + 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'. -38.5 + 3x + x2 = 0 Move the constant term to the right: Add '38.5' to each side of the equation. -38.5 + 3x + 38.5 + x2 = 0 + 38.5 Reorder the terms: -38.5 + 38.5 + 3x + x2 = 0 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + 3x + x2 = 0 + 38.5 3x + x2 = 0 + 38.5 Combine like terms: 0 + 38.5 = 38.5 3x + x2 = 38.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 38.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 38.5 + 2.25 Combine like terms: 38.5 + 2.25 = 40.75 2.25 + 3x + x2 = 40.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 40.75 Calculate the square root of the right side: 6.383572667 Break this problem into two subproblems by setting (x + 1.5) equal to 6.383572667 and -6.383572667.Subproblem 1
x + 1.5 = 6.383572667 Simplifying x + 1.5 = 6.383572667 Reorder the terms: 1.5 + x = 6.383572667 Solving 1.5 + x = 6.383572667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 6.383572667 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.383572667 + -1.5 x = 6.383572667 + -1.5 Combine like terms: 6.383572667 + -1.5 = 4.883572667 x = 4.883572667 Simplifying x = 4.883572667Subproblem 2
x + 1.5 = -6.383572667 Simplifying x + 1.5 = -6.383572667 Reorder the terms: 1.5 + x = -6.383572667 Solving 1.5 + x = -6.383572667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -6.383572667 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.383572667 + -1.5 x = -6.383572667 + -1.5 Combine like terms: -6.383572667 + -1.5 = -7.883572667 x = -7.883572667 Simplifying x = -7.883572667Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.883572667, -7.883572667}
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