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Simplifying 9x2 + 45x + -500 = 0 Reorder the terms: -500 + 45x + 9x2 = 0 Solving -500 + 45x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -55.55555556 + 5x + x2 = 0 Move the constant term to the right: Add '55.55555556' to each side of the equation. -55.55555556 + 5x + 55.55555556 + x2 = 0 + 55.55555556 Reorder the terms: -55.55555556 + 55.55555556 + 5x + x2 = 0 + 55.55555556 Combine like terms: -55.55555556 + 55.55555556 = 0.00000000 0.00000000 + 5x + x2 = 0 + 55.55555556 5x + x2 = 0 + 55.55555556 Combine like terms: 0 + 55.55555556 = 55.55555556 5x + x2 = 55.55555556 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 55.55555556 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 55.55555556 + 6.25 Combine like terms: 55.55555556 + 6.25 = 61.80555556 6.25 + 5x + x2 = 61.80555556 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 61.80555556 Calculate the square root of the right side: 7.861650944 Break this problem into two subproblems by setting (x + 2.5) equal to 7.861650944 and -7.861650944.Subproblem 1
x + 2.5 = 7.861650944 Simplifying x + 2.5 = 7.861650944 Reorder the terms: 2.5 + x = 7.861650944 Solving 2.5 + x = 7.861650944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 7.861650944 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.861650944 + -2.5 x = 7.861650944 + -2.5 Combine like terms: 7.861650944 + -2.5 = 5.361650944 x = 5.361650944 Simplifying x = 5.361650944Subproblem 2
x + 2.5 = -7.861650944 Simplifying x + 2.5 = -7.861650944 Reorder the terms: 2.5 + x = -7.861650944 Solving 2.5 + x = -7.861650944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -7.861650944 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.861650944 + -2.5 x = -7.861650944 + -2.5 Combine like terms: -7.861650944 + -2.5 = -10.361650944 x = -10.361650944 Simplifying x = -10.361650944Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.361650944, -10.361650944}
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