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Simplifying 0.05x2 + -0.3x + 0.07 = 0 Reorder the terms: 0.07 + -0.3x + 0.05x2 = 0 Solving 0.07 + -0.3x + 0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 1.4 + -6x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -6x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -6x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -6x + x2 = 0 + -1.4 -6x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -6x + x2 = -1.4 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -1.4 + 9 Reorder the terms: 9 + -6x + x2 = -1.4 + 9 Combine like terms: -1.4 + 9 = 7.6 9 + -6x + x2 = 7.6 Factor a perfect square on the left side: (x + -3)(x + -3) = 7.6 Calculate the square root of the right side: 2.75680975 Break this problem into two subproblems by setting (x + -3) equal to 2.75680975 and -2.75680975.Subproblem 1
x + -3 = 2.75680975 Simplifying x + -3 = 2.75680975 Reorder the terms: -3 + x = 2.75680975 Solving -3 + x = 2.75680975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.75680975 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.75680975 + 3 x = 2.75680975 + 3 Combine like terms: 2.75680975 + 3 = 5.75680975 x = 5.75680975 Simplifying x = 5.75680975Subproblem 2
x + -3 = -2.75680975 Simplifying x + -3 = -2.75680975 Reorder the terms: -3 + x = -2.75680975 Solving -3 + x = -2.75680975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.75680975 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.75680975 + 3 x = -2.75680975 + 3 Combine like terms: -2.75680975 + 3 = 0.24319025 x = 0.24319025 Simplifying x = 0.24319025Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.75680975, 0.24319025}
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