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Simplifying 45x2 + 2x + -30 = 0 Reorder the terms: -30 + 2x + 45x2 = 0 Solving -30 + 2x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.6666666667 + 0.04444444444x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.04444444444x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.04444444444x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.04444444444x + x2 = 0 + 0.6666666667 0.04444444444x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.04444444444x + x2 = 0.6666666667 The x term is 0.04444444444x. Take half its coefficient (0.02222222222). Square it (0.0004938271604) and add it to both sides. Add '0.0004938271604' to each side of the equation. 0.04444444444x + 0.0004938271604 + x2 = 0.6666666667 + 0.0004938271604 Reorder the terms: 0.0004938271604 + 0.04444444444x + x2 = 0.6666666667 + 0.0004938271604 Combine like terms: 0.6666666667 + 0.0004938271604 = 0.6671604938604 0.0004938271604 + 0.04444444444x + x2 = 0.6671604938604 Factor a perfect square on the left side: (x + 0.02222222222)(x + 0.02222222222) = 0.6671604938604 Calculate the square root of the right side: 0.816798931 Break this problem into two subproblems by setting (x + 0.02222222222) equal to 0.816798931 and -0.816798931.Subproblem 1
x + 0.02222222222 = 0.816798931 Simplifying x + 0.02222222222 = 0.816798931 Reorder the terms: 0.02222222222 + x = 0.816798931 Solving 0.02222222222 + x = 0.816798931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02222222222' to each side of the equation. 0.02222222222 + -0.02222222222 + x = 0.816798931 + -0.02222222222 Combine like terms: 0.02222222222 + -0.02222222222 = 0.00000000000 0.00000000000 + x = 0.816798931 + -0.02222222222 x = 0.816798931 + -0.02222222222 Combine like terms: 0.816798931 + -0.02222222222 = 0.79457670878 x = 0.79457670878 Simplifying x = 0.79457670878Subproblem 2
x + 0.02222222222 = -0.816798931 Simplifying x + 0.02222222222 = -0.816798931 Reorder the terms: 0.02222222222 + x = -0.816798931 Solving 0.02222222222 + x = -0.816798931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02222222222' to each side of the equation. 0.02222222222 + -0.02222222222 + x = -0.816798931 + -0.02222222222 Combine like terms: 0.02222222222 + -0.02222222222 = 0.00000000000 0.00000000000 + x = -0.816798931 + -0.02222222222 x = -0.816798931 + -0.02222222222 Combine like terms: -0.816798931 + -0.02222222222 = -0.83902115322 x = -0.83902115322 Simplifying x = -0.83902115322Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.79457670878, -0.83902115322}
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