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Simplifying 14x2 + 20x + -30 = 0 Reorder the terms: -30 + 20x + 14x2 = 0 Solving -30 + 20x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 10x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + 10x + 7x2)' equal to zero and attempt to solve: Simplifying -15 + 10x + 7x2 = 0 Solving -15 + 10x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.142857143 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + 1.428571429x + 2.142857143 + x2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + 1.428571429x + x2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + 1.428571429x + x2 = 0 + 2.142857143 1.428571429x + x2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 1.428571429x + x2 = 2.142857143 The x term is 1.428571429x. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429x + 0.5102040819 + x2 = 2.142857143 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 2.142857143 + 0.5102040819 Combine like terms: 2.142857143 + 0.5102040819 = 2.6530612249 0.5102040819 + 1.428571429x + x2 = 2.6530612249 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 2.6530612249 Calculate the square root of the right side: 1.628822036 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 1.628822036 and -1.628822036.Subproblem 1
x + 0.7142857145 = 1.628822036 Simplifying x + 0.7142857145 = 1.628822036 Reorder the terms: 0.7142857145 + x = 1.628822036 Solving 0.7142857145 + x = 1.628822036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 1.628822036 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 1.628822036 + -0.7142857145 x = 1.628822036 + -0.7142857145 Combine like terms: 1.628822036 + -0.7142857145 = 0.9145363215 x = 0.9145363215 Simplifying x = 0.9145363215Subproblem 2
x + 0.7142857145 = -1.628822036 Simplifying x + 0.7142857145 = -1.628822036 Reorder the terms: 0.7142857145 + x = -1.628822036 Solving 0.7142857145 + x = -1.628822036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -1.628822036 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -1.628822036 + -0.7142857145 x = -1.628822036 + -0.7142857145 Combine like terms: -1.628822036 + -0.7142857145 = -2.3431077505 x = -2.3431077505 Simplifying x = -2.3431077505Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9145363215, -2.3431077505}Solution
x = {0.9145363215, -2.3431077505}
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