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Simplifying 1 = 0.01x2 + -0.44x Reorder the terms: 1 = -0.44x + 0.01x2 Solving 1 = -0.44x + 0.01x2 Solving for variable 'x'. Reorder the terms: 1 + 0.44x + -0.01x2 = -0.44x + 0.44x + 0.01x2 + -0.01x2 Combine like terms: -0.44x + 0.44x = 0.00 1 + 0.44x + -0.01x2 = 0.00 + 0.01x2 + -0.01x2 1 + 0.44x + -0.01x2 = 0.01x2 + -0.01x2 Combine like terms: 0.01x2 + -0.01x2 = 0.00 1 + 0.44x + -0.01x2 = 0.00 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -100 + -44x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -44x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -44x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -44x + x2 = 0 + 100 -44x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -44x + x2 = 100 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = 100 + 484 Reorder the terms: 484 + -44x + x2 = 100 + 484 Combine like terms: 100 + 484 = 584 484 + -44x + x2 = 584 Factor a perfect square on the left side: (x + -22)(x + -22) = 584 Calculate the square root of the right side: 24.166091947 Break this problem into two subproblems by setting (x + -22) equal to 24.166091947 and -24.166091947.Subproblem 1
x + -22 = 24.166091947 Simplifying x + -22 = 24.166091947 Reorder the terms: -22 + x = 24.166091947 Solving -22 + x = 24.166091947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 24.166091947 + 22 Combine like terms: -22 + 22 = 0 0 + x = 24.166091947 + 22 x = 24.166091947 + 22 Combine like terms: 24.166091947 + 22 = 46.166091947 x = 46.166091947 Simplifying x = 46.166091947Subproblem 2
x + -22 = -24.166091947 Simplifying x + -22 = -24.166091947 Reorder the terms: -22 + x = -24.166091947 Solving -22 + x = -24.166091947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -24.166091947 + 22 Combine like terms: -22 + 22 = 0 0 + x = -24.166091947 + 22 x = -24.166091947 + 22 Combine like terms: -24.166091947 + 22 = -2.166091947 x = -2.166091947 Simplifying x = -2.166091947Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.166091947, -2.166091947}
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