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Simplifying 2x * x + 5x + -56 = 0 Multiply x * x 2x2 + 5x + -56 = 0 Reorder the terms: -56 + 5x + 2x2 = 0 Solving -56 + 5x + 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'. -28 + 2.5x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 2.5x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 2.5x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 2.5x + x2 = 0 + 28 2.5x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 2.5x + x2 = 28 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 28 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 28 + 1.5625 Combine like terms: 28 + 1.5625 = 29.5625 1.5625 + 2.5x + x2 = 29.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 29.5625 Calculate the square root of the right side: 5.437140793 Break this problem into two subproblems by setting (x + 1.25) equal to 5.437140793 and -5.437140793.Subproblem 1
x + 1.25 = 5.437140793 Simplifying x + 1.25 = 5.437140793 Reorder the terms: 1.25 + x = 5.437140793 Solving 1.25 + x = 5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 5.437140793 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 5.437140793 + -1.25 x = 5.437140793 + -1.25 Combine like terms: 5.437140793 + -1.25 = 4.187140793 x = 4.187140793 Simplifying x = 4.187140793Subproblem 2
x + 1.25 = -5.437140793 Simplifying x + 1.25 = -5.437140793 Reorder the terms: 1.25 + x = -5.437140793 Solving 1.25 + x = -5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -5.437140793 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -5.437140793 + -1.25 x = -5.437140793 + -1.25 Combine like terms: -5.437140793 + -1.25 = -6.687140793 x = -6.687140793 Simplifying x = -6.687140793Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.187140793, -6.687140793}
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