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Simplifying 0.0001x2 + 0.02x + -1.9 = 0.17 Reorder the terms: -1.9 + 0.02x + 0.0001x2 = 0.17 Solving -1.9 + 0.02x + 0.0001x2 = 0.17 Solving for variable 'x'. Reorder the terms: -1.9 + -0.17 + 0.02x + 0.0001x2 = 0.17 + -0.17 Combine like terms: -1.9 + -0.17 = -2.07 -2.07 + 0.02x + 0.0001x2 = 0.17 + -0.17 Combine like terms: 0.17 + -0.17 = 0.00 -2.07 + 0.02x + 0.0001x2 = 0.00 Begin completing the square. Divide all terms by 0.0001 the coefficient of the squared term: Divide each side by '0.0001'. -20700 + 200x + x2 = 0 Move the constant term to the right: Add '20700' to each side of the equation. -20700 + 200x + 20700 + x2 = 0 + 20700 Reorder the terms: -20700 + 20700 + 200x + x2 = 0 + 20700 Combine like terms: -20700 + 20700 = 0 0 + 200x + x2 = 0 + 20700 200x + x2 = 0 + 20700 Combine like terms: 0 + 20700 = 20700 200x + x2 = 20700 The x term is 200x. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200x + 10000 + x2 = 20700 + 10000 Reorder the terms: 10000 + 200x + x2 = 20700 + 10000 Combine like terms: 20700 + 10000 = 30700 10000 + 200x + x2 = 30700 Factor a perfect square on the left side: (x + 100)(x + 100) = 30700 Calculate the square root of the right side: 175.214154679 Break this problem into two subproblems by setting (x + 100) equal to 175.214154679 and -175.214154679.Subproblem 1
x + 100 = 175.214154679 Simplifying x + 100 = 175.214154679 Reorder the terms: 100 + x = 175.214154679 Solving 100 + x = 175.214154679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 175.214154679 + -100 Combine like terms: 100 + -100 = 0 0 + x = 175.214154679 + -100 x = 175.214154679 + -100 Combine like terms: 175.214154679 + -100 = 75.214154679 x = 75.214154679 Simplifying x = 75.214154679Subproblem 2
x + 100 = -175.214154679 Simplifying x + 100 = -175.214154679 Reorder the terms: 100 + x = -175.214154679 Solving 100 + x = -175.214154679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = -175.214154679 + -100 Combine like terms: 100 + -100 = 0 0 + x = -175.214154679 + -100 x = -175.214154679 + -100 Combine like terms: -175.214154679 + -100 = -275.214154679 x = -275.214154679 Simplifying x = -275.214154679Solution
The solution to the problem is based on the solutions from the subproblems. x = {75.214154679, -275.214154679}
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