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Simplifying 5x2 + -18x + -75 = 0 Reorder the terms: -75 + -18x + 5x2 = 0 Solving -75 + -18x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -15 + -3.6x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -3.6x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -3.6x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -3.6x + x2 = 0 + 15 -3.6x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -3.6x + x2 = 15 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = 15 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 15 + 3.24 Combine like terms: 15 + 3.24 = 18.24 3.24 + -3.6x + x2 = 18.24 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 18.24 Calculate the square root of the right side: 4.270831301 Break this problem into two subproblems by setting (x + -1.8) equal to 4.270831301 and -4.270831301.Subproblem 1
x + -1.8 = 4.270831301 Simplifying x + -1.8 = 4.270831301 Reorder the terms: -1.8 + x = 4.270831301 Solving -1.8 + x = 4.270831301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 4.270831301 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 4.270831301 + 1.8 x = 4.270831301 + 1.8 Combine like terms: 4.270831301 + 1.8 = 6.070831301 x = 6.070831301 Simplifying x = 6.070831301Subproblem 2
x + -1.8 = -4.270831301 Simplifying x + -1.8 = -4.270831301 Reorder the terms: -1.8 + x = -4.270831301 Solving -1.8 + x = -4.270831301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -4.270831301 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -4.270831301 + 1.8 x = -4.270831301 + 1.8 Combine like terms: -4.270831301 + 1.8 = -2.470831301 x = -2.470831301 Simplifying x = -2.470831301Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.070831301, -2.470831301}
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