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Simplifying 5x2 + 45x + -10 = 0 Reorder the terms: -10 + 45x + 5x2 = 0 Solving -10 + 45x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + 9x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + 9x + x2)' equal to zero and attempt to solve: Simplifying -2 + 9x + x2 = 0 Solving -2 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 9x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 9x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 9x + x2 = 0 + 2 9x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 9x + x2 = 2 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 2 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 2 + 20.25 Combine like terms: 2 + 20.25 = 22.25 20.25 + 9x + x2 = 22.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + 4.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + 4.5 = 4.716990566 Simplifying x + 4.5 = 4.716990566 Reorder the terms: 4.5 + x = 4.716990566 Solving 4.5 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.716990566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.716990566 + -4.5 x = 4.716990566 + -4.5 Combine like terms: 4.716990566 + -4.5 = 0.216990566 x = 0.216990566 Simplifying x = 0.216990566Subproblem 2
x + 4.5 = -4.716990566 Simplifying x + 4.5 = -4.716990566 Reorder the terms: 4.5 + x = -4.716990566 Solving 4.5 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.716990566 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.716990566 + -4.5 x = -4.716990566 + -4.5 Combine like terms: -4.716990566 + -4.5 = -9.216990566 x = -9.216990566 Simplifying x = -9.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.216990566, -9.216990566}Solution
x = {0.216990566, -9.216990566}
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