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Simplifying 30x2 + 63x + -20 = 0 Reorder the terms: -20 + 63x + 30x2 = 0 Solving -20 + 63x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.6666666667 + 2.1x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 2.1x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 2.1x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 2.1x + x2 = 0 + 0.6666666667 2.1x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 2.1x + x2 = 0.6666666667 The x term is 2.1x. Take half its coefficient (1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. 2.1x + 1.1025 + x2 = 0.6666666667 + 1.1025 Reorder the terms: 1.1025 + 2.1x + x2 = 0.6666666667 + 1.1025 Combine like terms: 0.6666666667 + 1.1025 = 1.7691666667 1.1025 + 2.1x + x2 = 1.7691666667 Factor a perfect square on the left side: (x + 1.05)(x + 1.05) = 1.7691666667 Calculate the square root of the right side: 1.330100247 Break this problem into two subproblems by setting (x + 1.05) equal to 1.330100247 and -1.330100247.Subproblem 1
x + 1.05 = 1.330100247 Simplifying x + 1.05 = 1.330100247 Reorder the terms: 1.05 + x = 1.330100247 Solving 1.05 + x = 1.330100247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + x = 1.330100247 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + x = 1.330100247 + -1.05 x = 1.330100247 + -1.05 Combine like terms: 1.330100247 + -1.05 = 0.280100247 x = 0.280100247 Simplifying x = 0.280100247Subproblem 2
x + 1.05 = -1.330100247 Simplifying x + 1.05 = -1.330100247 Reorder the terms: 1.05 + x = -1.330100247 Solving 1.05 + x = -1.330100247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + x = -1.330100247 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + x = -1.330100247 + -1.05 x = -1.330100247 + -1.05 Combine like terms: -1.330100247 + -1.05 = -2.380100247 x = -2.380100247 Simplifying x = -2.380100247Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.280100247, -2.380100247}
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