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Simplifying x(2x + -5) = 45 Reorder the terms: x(-5 + 2x) = 45 (-5 * x + 2x * x) = 45 (-5x + 2x2) = 45 Solving -5x + 2x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -5x + 2x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -2.5x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -2.5x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -2.5x + x2 = 0 + 22.5 -2.5x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -2.5x + x2 = 22.5 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 = 22.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 22.5 + 1.5625 Combine like terms: 22.5 + 1.5625 = 24.0625 1.5625 + -2.5x + x2 = 24.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (x + -1.25) equal to 4.905354218 and -4.905354218.Subproblem 1
x + -1.25 = 4.905354218 Simplifying x + -1.25 = 4.905354218 Reorder the terms: -1.25 + x = 4.905354218 Solving -1.25 + x = 4.905354218 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 = 4.905354218 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 4.905354218 + 1.25 x = 4.905354218 + 1.25 Combine like terms: 4.905354218 + 1.25 = 6.155354218 x = 6.155354218 Simplifying x = 6.155354218Subproblem 2
x + -1.25 = -4.905354218 Simplifying x + -1.25 = -4.905354218 Reorder the terms: -1.25 + x = -4.905354218 Solving -1.25 + x = -4.905354218 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 = -4.905354218 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -4.905354218 + 1.25 x = -4.905354218 + 1.25 Combine like terms: -4.905354218 + 1.25 = -3.655354218 x = -3.655354218 Simplifying x = -3.655354218Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.155354218, -3.655354218}
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