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Simplifying 5x + 50 = 0.9x2 Reorder the terms: 50 + 5x = 0.9x2 Solving 50 + 5x = 0.9x2 Solving for variable 'x'. Combine like terms: 0.9x2 + -0.9x2 = 0.0 50 + 5x + -0.9x2 = 0.0 Begin completing the square. Divide all terms by -0.9 the coefficient of the squared term: Divide each side by '-0.9'. -55.55555556 + -5.555555556x + x2 = 0 Move the constant term to the right: Add '55.55555556' to each side of the equation. -55.55555556 + -5.555555556x + 55.55555556 + x2 = 0 + 55.55555556 Reorder the terms: -55.55555556 + 55.55555556 + -5.555555556x + x2 = 0 + 55.55555556 Combine like terms: -55.55555556 + 55.55555556 = 0.00000000 0.00000000 + -5.555555556x + x2 = 0 + 55.55555556 -5.555555556x + x2 = 0 + 55.55555556 Combine like terms: 0 + 55.55555556 = 55.55555556 -5.555555556x + x2 = 55.55555556 The x term is -5.555555556x. Take half its coefficient (-2.777777778). Square it (7.716049384) and add it to both sides. Add '7.716049384' to each side of the equation. -5.555555556x + 7.716049384 + x2 = 55.55555556 + 7.716049384 Reorder the terms: 7.716049384 + -5.555555556x + x2 = 55.55555556 + 7.716049384 Combine like terms: 55.55555556 + 7.716049384 = 63.271604944 7.716049384 + -5.555555556x + x2 = 63.271604944 Factor a perfect square on the left side: (x + -2.777777778)(x + -2.777777778) = 63.271604944 Calculate the square root of the right side: 7.954345036 Break this problem into two subproblems by setting (x + -2.777777778) equal to 7.954345036 and -7.954345036.Subproblem 1
x + -2.777777778 = 7.954345036 Simplifying x + -2.777777778 = 7.954345036 Reorder the terms: -2.777777778 + x = 7.954345036 Solving -2.777777778 + x = 7.954345036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = 7.954345036 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = 7.954345036 + 2.777777778 x = 7.954345036 + 2.777777778 Combine like terms: 7.954345036 + 2.777777778 = 10.732122814 x = 10.732122814 Simplifying x = 10.732122814Subproblem 2
x + -2.777777778 = -7.954345036 Simplifying x + -2.777777778 = -7.954345036 Reorder the terms: -2.777777778 + x = -7.954345036 Solving -2.777777778 + x = -7.954345036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = -7.954345036 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = -7.954345036 + 2.777777778 x = -7.954345036 + 2.777777778 Combine like terms: -7.954345036 + 2.777777778 = -5.176567258 x = -5.176567258 Simplifying x = -5.176567258Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.732122814, -5.176567258}
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