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Simplifying 5x2 + -10x + -225 = 0 Reorder the terms: -225 + -10x + 5x2 = 0 Solving -225 + -10x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-45 + -2x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-45 + -2x + x2)' equal to zero and attempt to solve: Simplifying -45 + -2x + x2 = 0 Solving -45 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -2x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + -2x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -2x + x2 = 0 + 45 -2x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 -2x + x2 = 45 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 45 + 1 Reorder the terms: 1 + -2x + x2 = 45 + 1 Combine like terms: 45 + 1 = 46 1 + -2x + x2 = 46 Factor a perfect square on the left side: (x + -1)(x + -1) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + -1) equal to 6.782329983 and -6.782329983.Subproblem 1
x + -1 = 6.782329983 Simplifying x + -1 = 6.782329983 Reorder the terms: -1 + x = 6.782329983 Solving -1 + x = 6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 6.782329983 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.782329983 + 1 x = 6.782329983 + 1 Combine like terms: 6.782329983 + 1 = 7.782329983 x = 7.782329983 Simplifying x = 7.782329983Subproblem 2
x + -1 = -6.782329983 Simplifying x + -1 = -6.782329983 Reorder the terms: -1 + x = -6.782329983 Solving -1 + x = -6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -6.782329983 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.782329983 + 1 x = -6.782329983 + 1 Combine like terms: -6.782329983 + 1 = -5.782329983 x = -5.782329983 Simplifying x = -5.782329983Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.782329983, -5.782329983}Solution
x = {7.782329983, -5.782329983}
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