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Simplifying 5x2 + -12x + -45 = 0 Reorder the terms: -45 + -12x + 5x2 = 0 Solving -45 + -12x + 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'. -9 + -2.4x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -2.4x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -2.4x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2.4x + x2 = 0 + 9 -2.4x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2.4x + x2 = 9 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 9 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 9 + 1.44 Combine like terms: 9 + 1.44 = 10.44 1.44 + -2.4x + x2 = 10.44 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 10.44 Calculate the square root of the right side: 3.231098884 Break this problem into two subproblems by setting (x + -1.2) equal to 3.231098884 and -3.231098884.Subproblem 1
x + -1.2 = 3.231098884 Simplifying x + -1.2 = 3.231098884 Reorder the terms: -1.2 + x = 3.231098884 Solving -1.2 + x = 3.231098884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 3.231098884 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 3.231098884 + 1.2 x = 3.231098884 + 1.2 Combine like terms: 3.231098884 + 1.2 = 4.431098884 x = 4.431098884 Simplifying x = 4.431098884Subproblem 2
x + -1.2 = -3.231098884 Simplifying x + -1.2 = -3.231098884 Reorder the terms: -1.2 + x = -3.231098884 Solving -1.2 + x = -3.231098884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -3.231098884 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -3.231098884 + 1.2 x = -3.231098884 + 1.2 Combine like terms: -3.231098884 + 1.2 = -2.031098884 x = -2.031098884 Simplifying x = -2.031098884Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.431098884, -2.031098884}
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