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Simplifying x(2x + -5) = 38 Reorder the terms: x(-5 + 2x) = 38 (-5 * x + 2x * x) = 38 (-5x + 2x2) = 38 Solving -5x + 2x2 = 38 Solving for variable 'x'. Reorder the terms: -38 + -5x + 2x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19 + -2.5x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + -2.5x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -2.5x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -2.5x + x2 = 0 + 19 -2.5x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -2.5x + x2 = 19 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 = 19 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 19 + 1.5625 Combine like terms: 19 + 1.5625 = 20.5625 1.5625 + -2.5x + x2 = 20.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (x + -1.25) equal to 4.534589287 and -4.534589287.Subproblem 1
x + -1.25 = 4.534589287 Simplifying x + -1.25 = 4.534589287 Reorder the terms: -1.25 + x = 4.534589287 Solving -1.25 + x = 4.534589287 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 = 4.534589287 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 4.534589287 + 1.25 x = 4.534589287 + 1.25 Combine like terms: 4.534589287 + 1.25 = 5.784589287 x = 5.784589287 Simplifying x = 5.784589287Subproblem 2
x + -1.25 = -4.534589287 Simplifying x + -1.25 = -4.534589287 Reorder the terms: -1.25 + x = -4.534589287 Solving -1.25 + x = -4.534589287 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 = -4.534589287 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -4.534589287 + 1.25 x = -4.534589287 + 1.25 Combine like terms: -4.534589287 + 1.25 = -3.284589287 x = -3.284589287 Simplifying x = -3.284589287Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.784589287, -3.284589287}
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