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Simplifying -0.006x2 + 1.2x + 10 = 1 Reorder the terms: 10 + 1.2x + -0.006x2 = 1 Solving 10 + 1.2x + -0.006x2 = 1 Solving for variable 'x'. Reorder the terms: 10 + -1 + 1.2x + -0.006x2 = 1 + -1 Combine like terms: 10 + -1 = 9 9 + 1.2x + -0.006x2 = 1 + -1 Combine like terms: 1 + -1 = 0 9 + 1.2x + -0.006x2 = 0 Begin completing the square. Divide all terms by -0.006 the coefficient of the squared term: Divide each side by '-0.006'. -1500 + -200x + x2 = 0 Move the constant term to the right: Add '1500' to each side of the equation. -1500 + -200x + 1500 + x2 = 0 + 1500 Reorder the terms: -1500 + 1500 + -200x + x2 = 0 + 1500 Combine like terms: -1500 + 1500 = 0 0 + -200x + x2 = 0 + 1500 -200x + x2 = 0 + 1500 Combine like terms: 0 + 1500 = 1500 -200x + x2 = 1500 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 = 1500 + 10000 Reorder the terms: 10000 + -200x + x2 = 1500 + 10000 Combine like terms: 1500 + 10000 = 11500 10000 + -200x + x2 = 11500 Factor a perfect square on the left side: (x + -100)(x + -100) = 11500 Calculate the square root of the right side: 107.238052948 Break this problem into two subproblems by setting (x + -100) equal to 107.238052948 and -107.238052948.Subproblem 1
x + -100 = 107.238052948 Simplifying x + -100 = 107.238052948 Reorder the terms: -100 + x = 107.238052948 Solving -100 + x = 107.238052948 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 = 107.238052948 + 100 Combine like terms: -100 + 100 = 0 0 + x = 107.238052948 + 100 x = 107.238052948 + 100 Combine like terms: 107.238052948 + 100 = 207.238052948 x = 207.238052948 Simplifying x = 207.238052948Subproblem 2
x + -100 = -107.238052948 Simplifying x + -100 = -107.238052948 Reorder the terms: -100 + x = -107.238052948 Solving -100 + x = -107.238052948 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 = -107.238052948 + 100 Combine like terms: -100 + 100 = 0 0 + x = -107.238052948 + 100 x = -107.238052948 + 100 Combine like terms: -107.238052948 + 100 = -7.238052948 x = -7.238052948 Simplifying x = -7.238052948Solution
The solution to the problem is based on the solutions from the subproblems. x = {207.238052948, -7.238052948}
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