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Simplifying 0.09x2 + 5x + 5 = 0 Reorder the terms: 5 + 5x + 0.09x2 = 0 Solving 5 + 5x + 0.09x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.09 the coefficient of the squared term: Divide each side by '0.09'. 55.55555556 + 55.55555556x + x2 = 0 Move the constant term to the right: Add '-55.55555556' to each side of the equation. 55.55555556 + 55.55555556x + -55.55555556 + x2 = 0 + -55.55555556 Reorder the terms: 55.55555556 + -55.55555556 + 55.55555556x + x2 = 0 + -55.55555556 Combine like terms: 55.55555556 + -55.55555556 = 0.00000000 0.00000000 + 55.55555556x + x2 = 0 + -55.55555556 55.55555556x + x2 = 0 + -55.55555556 Combine like terms: 0 + -55.55555556 = -55.55555556 55.55555556x + x2 = -55.55555556 The x term is 55.55555556x. Take half its coefficient (27.77777778). Square it (771.6049384) and add it to both sides. Add '771.6049384' to each side of the equation. 55.55555556x + 771.6049384 + x2 = -55.55555556 + 771.6049384 Reorder the terms: 771.6049384 + 55.55555556x + x2 = -55.55555556 + 771.6049384 Combine like terms: -55.55555556 + 771.6049384 = 716.04938284 771.6049384 + 55.55555556x + x2 = 716.04938284 Factor a perfect square on the left side: (x + 27.77777778)(x + 27.77777778) = 716.04938284 Calculate the square root of the right side: 26.759099066 Break this problem into two subproblems by setting (x + 27.77777778) equal to 26.759099066 and -26.759099066.Subproblem 1
x + 27.77777778 = 26.759099066 Simplifying x + 27.77777778 = 26.759099066 Reorder the terms: 27.77777778 + x = 26.759099066 Solving 27.77777778 + x = 26.759099066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.77777778' to each side of the equation. 27.77777778 + -27.77777778 + x = 26.759099066 + -27.77777778 Combine like terms: 27.77777778 + -27.77777778 = 0.00000000 0.00000000 + x = 26.759099066 + -27.77777778 x = 26.759099066 + -27.77777778 Combine like terms: 26.759099066 + -27.77777778 = -1.018678714 x = -1.018678714 Simplifying x = -1.018678714Subproblem 2
x + 27.77777778 = -26.759099066 Simplifying x + 27.77777778 = -26.759099066 Reorder the terms: 27.77777778 + x = -26.759099066 Solving 27.77777778 + x = -26.759099066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.77777778' to each side of the equation. 27.77777778 + -27.77777778 + x = -26.759099066 + -27.77777778 Combine like terms: 27.77777778 + -27.77777778 = 0.00000000 0.00000000 + x = -26.759099066 + -27.77777778 x = -26.759099066 + -27.77777778 Combine like terms: -26.759099066 + -27.77777778 = -54.536876846 x = -54.536876846 Simplifying x = -54.536876846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.018678714, -54.536876846}
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