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Simplifying 0.1x + -0.05x(x + -20) = 1.2 Reorder the terms: 0.1x + -0.05x(-20 + x) = 1.2 0.1x + (-20 * -0.05x + x * -0.05x) = 1.2 0.1x + (1x + -0.05x2) = 1.2 Combine like terms: 0.1x + 1x = 1.1x 1.1x + -0.05x2 = 1.2 Solving 1.1x + -0.05x2 = 1.2 Solving for variable 'x'. Reorder the terms: -1.2 + 1.1x + -0.05x2 = 1.2 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 -1.2 + 1.1x + -0.05x2 = 0.0 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. 24 + -22x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -22x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -22x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -22x + x2 = 0 + -24 -22x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -22x + x2 = -24 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = -24 + 121 Reorder the terms: 121 + -22x + x2 = -24 + 121 Combine like terms: -24 + 121 = 97 121 + -22x + x2 = 97 Factor a perfect square on the left side: (x + -11)(x + -11) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + -11) equal to 9.848857802 and -9.848857802.Subproblem 1
x + -11 = 9.848857802 Simplifying x + -11 = 9.848857802 Reorder the terms: -11 + x = 9.848857802 Solving -11 + x = 9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 9.848857802 + 11 Combine like terms: -11 + 11 = 0 0 + x = 9.848857802 + 11 x = 9.848857802 + 11 Combine like terms: 9.848857802 + 11 = 20.848857802 x = 20.848857802 Simplifying x = 20.848857802Subproblem 2
x + -11 = -9.848857802 Simplifying x + -11 = -9.848857802 Reorder the terms: -11 + x = -9.848857802 Solving -11 + x = -9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -9.848857802 + 11 Combine like terms: -11 + 11 = 0 0 + x = -9.848857802 + 11 x = -9.848857802 + 11 Combine like terms: -9.848857802 + 11 = 1.151142198 x = 1.151142198 Simplifying x = 1.151142198Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.848857802, 1.151142198}
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