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Simplifying x(2x + -9) = 49 Reorder the terms: x(-9 + 2x) = 49 (-9 * x + 2x * x) = 49 (-9x + 2x2) = 49 Solving -9x + 2x2 = 49 Solving for variable 'x'. Reorder the terms: -49 + -9x + 2x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + -4.5x + 24.5 + x2 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + -4.5x + x2 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + -4.5x + x2 = 0 + 24.5 -4.5x + x2 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 -4.5x + x2 = 24.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 24.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 24.5 + 5.0625 Combine like terms: 24.5 + 5.0625 = 29.5625 5.0625 + -4.5x + x2 = 29.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 29.5625 Calculate the square root of the right side: 5.437140793 Break this problem into two subproblems by setting (x + -2.25) equal to 5.437140793 and -5.437140793.Subproblem 1
x + -2.25 = 5.437140793 Simplifying x + -2.25 = 5.437140793 Reorder the terms: -2.25 + x = 5.437140793 Solving -2.25 + x = 5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 5.437140793 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 5.437140793 + 2.25 x = 5.437140793 + 2.25 Combine like terms: 5.437140793 + 2.25 = 7.687140793 x = 7.687140793 Simplifying x = 7.687140793Subproblem 2
x + -2.25 = -5.437140793 Simplifying x + -2.25 = -5.437140793 Reorder the terms: -2.25 + x = -5.437140793 Solving -2.25 + x = -5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -5.437140793 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -5.437140793 + 2.25 x = -5.437140793 + 2.25 Combine like terms: -5.437140793 + 2.25 = -3.187140793 x = -3.187140793 Simplifying x = -3.187140793Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.687140793, -3.187140793}
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