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Simplifying (x + -2) * 180x = 8 Reorder the terms: (-2 + x) * 180x = 8 Reorder the terms for easier multiplication: 180x(-2 + x) = 8 (-2 * 180x + x * 180x) = 8 (-360x + 180x2) = 8 Solving -360x + 180x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -360x + 180x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -360x + 180x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + -90x + 45x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -90x + 45x2)' equal to zero and attempt to solve: Simplifying -2 + -90x + 45x2 = 0 Solving -2 + -90x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.04444444444 + -2x + x2 = 0 Move the constant term to the right: Add '0.04444444444' to each side of the equation. -0.04444444444 + -2x + 0.04444444444 + x2 = 0 + 0.04444444444 Reorder the terms: -0.04444444444 + 0.04444444444 + -2x + x2 = 0 + 0.04444444444 Combine like terms: -0.04444444444 + 0.04444444444 = 0.00000000000 0.00000000000 + -2x + x2 = 0 + 0.04444444444 -2x + x2 = 0 + 0.04444444444 Combine like terms: 0 + 0.04444444444 = 0.04444444444 -2x + x2 = 0.04444444444 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.04444444444 + 1 Reorder the terms: 1 + -2x + x2 = 0.04444444444 + 1 Combine like terms: 0.04444444444 + 1 = 1.04444444444 1 + -2x + x2 = 1.04444444444 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.04444444444 Calculate the square root of the right side: 1.021980648 Break this problem into two subproblems by setting (x + -1) equal to 1.021980648 and -1.021980648.Subproblem 1
x + -1 = 1.021980648 Simplifying x + -1 = 1.021980648 Reorder the terms: -1 + x = 1.021980648 Solving -1 + x = 1.021980648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.021980648 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.021980648 + 1 x = 1.021980648 + 1 Combine like terms: 1.021980648 + 1 = 2.021980648 x = 2.021980648 Simplifying x = 2.021980648Subproblem 2
x + -1 = -1.021980648 Simplifying x + -1 = -1.021980648 Reorder the terms: -1 + x = -1.021980648 Solving -1 + x = -1.021980648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.021980648 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.021980648 + 1 x = -1.021980648 + 1 Combine like terms: -1.021980648 + 1 = -0.021980648 x = -0.021980648 Simplifying x = -0.021980648Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.021980648, -0.021980648}Solution
x = {2.021980648, -0.021980648}
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