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Simplifying 3 + 0.1(4 + -1x) = 1.7x(0.4x + -3.4) 3 + (4 * 0.1 + -1x * 0.1) = 1.7x(0.4x + -3.4) 3 + (0.4 + -0.1x) = 1.7x(0.4x + -3.4) Combine like terms: 3 + 0.4 = 3.4 3.4 + -0.1x = 1.7x(0.4x + -3.4) Reorder the terms: 3.4 + -0.1x = 1.7x(-3.4 + 0.4x) 3.4 + -0.1x = (-3.4 * 1.7x + 0.4x * 1.7x) 3.4 + -0.1x = (-5.78x + 0.68x2) Solving 3.4 + -0.1x = -5.78x + 0.68x2 Solving for variable 'x'. Combine like terms: -0.1x + 5.78x = 5.68x 3.4 + 5.68x + -0.68x2 = -5.78x + 0.68x2 + 5.78x + -0.68x2 Reorder the terms: 3.4 + 5.68x + -0.68x2 = -5.78x + 5.78x + 0.68x2 + -0.68x2 Combine like terms: -5.78x + 5.78x = 0.00 3.4 + 5.68x + -0.68x2 = 0.00 + 0.68x2 + -0.68x2 3.4 + 5.68x + -0.68x2 = 0.68x2 + -0.68x2 Combine like terms: 0.68x2 + -0.68x2 = 0.00 3.4 + 5.68x + -0.68x2 = 0.00 Begin completing the square. Divide all terms by -0.68 the coefficient of the squared term: Divide each side by '-0.68'. -5 + -8.352941176x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -8.352941176x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -8.352941176x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8.352941176x + x2 = 0 + 5 -8.352941176x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -8.352941176x + x2 = 5 The x term is -8.352941176x. Take half its coefficient (-4.176470588). Square it (17.44290657) and add it to both sides. Add '17.44290657' to each side of the equation. -8.352941176x + 17.44290657 + x2 = 5 + 17.44290657 Reorder the terms: 17.44290657 + -8.352941176x + x2 = 5 + 17.44290657 Combine like terms: 5 + 17.44290657 = 22.44290657 17.44290657 + -8.352941176x + x2 = 22.44290657 Factor a perfect square on the left side: (x + -4.176470588)(x + -4.176470588) = 22.44290657 Calculate the square root of the right side: 4.737394492 Break this problem into two subproblems by setting (x + -4.176470588) equal to 4.737394492 and -4.737394492.Subproblem 1
x + -4.176470588 = 4.737394492 Simplifying x + -4.176470588 = 4.737394492 Reorder the terms: -4.176470588 + x = 4.737394492 Solving -4.176470588 + x = 4.737394492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.176470588' to each side of the equation. -4.176470588 + 4.176470588 + x = 4.737394492 + 4.176470588 Combine like terms: -4.176470588 + 4.176470588 = 0.000000000 0.000000000 + x = 4.737394492 + 4.176470588 x = 4.737394492 + 4.176470588 Combine like terms: 4.737394492 + 4.176470588 = 8.91386508 x = 8.91386508 Simplifying x = 8.91386508Subproblem 2
x + -4.176470588 = -4.737394492 Simplifying x + -4.176470588 = -4.737394492 Reorder the terms: -4.176470588 + x = -4.737394492 Solving -4.176470588 + x = -4.737394492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.176470588' to each side of the equation. -4.176470588 + 4.176470588 + x = -4.737394492 + 4.176470588 Combine like terms: -4.176470588 + 4.176470588 = 0.000000000 0.000000000 + x = -4.737394492 + 4.176470588 x = -4.737394492 + 4.176470588 Combine like terms: -4.737394492 + 4.176470588 = -0.560923904 x = -0.560923904 Simplifying x = -0.560923904Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.91386508, -0.560923904}
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