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Simplifying 70x2 + -121x + -30 = 0 Reorder the terms: -30 + -121x + 70x2 = 0 Solving -30 + -121x + 70x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 70 the coefficient of the squared term: Divide each side by '70'. -0.4285714286 + -1.728571429x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -1.728571429x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -1.728571429x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -1.728571429x + x2 = 0 + 0.4285714286 -1.728571429x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -1.728571429x + x2 = 0.4285714286 The x term is -1.728571429x. Take half its coefficient (-0.8642857145). Square it (0.7469897963) and add it to both sides. Add '0.7469897963' to each side of the equation. -1.728571429x + 0.7469897963 + x2 = 0.4285714286 + 0.7469897963 Reorder the terms: 0.7469897963 + -1.728571429x + x2 = 0.4285714286 + 0.7469897963 Combine like terms: 0.4285714286 + 0.7469897963 = 1.1755612249 0.7469897963 + -1.728571429x + x2 = 1.1755612249 Factor a perfect square on the left side: (x + -0.8642857145)(x + -0.8642857145) = 1.1755612249 Calculate the square root of the right side: 1.084233012 Break this problem into two subproblems by setting (x + -0.8642857145) equal to 1.084233012 and -1.084233012.Subproblem 1
x + -0.8642857145 = 1.084233012 Simplifying x + -0.8642857145 = 1.084233012 Reorder the terms: -0.8642857145 + x = 1.084233012 Solving -0.8642857145 + x = 1.084233012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8642857145' to each side of the equation. -0.8642857145 + 0.8642857145 + x = 1.084233012 + 0.8642857145 Combine like terms: -0.8642857145 + 0.8642857145 = 0.0000000000 0.0000000000 + x = 1.084233012 + 0.8642857145 x = 1.084233012 + 0.8642857145 Combine like terms: 1.084233012 + 0.8642857145 = 1.9485187265 x = 1.9485187265 Simplifying x = 1.9485187265Subproblem 2
x + -0.8642857145 = -1.084233012 Simplifying x + -0.8642857145 = -1.084233012 Reorder the terms: -0.8642857145 + x = -1.084233012 Solving -0.8642857145 + x = -1.084233012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8642857145' to each side of the equation. -0.8642857145 + 0.8642857145 + x = -1.084233012 + 0.8642857145 Combine like terms: -0.8642857145 + 0.8642857145 = 0.0000000000 0.0000000000 + x = -1.084233012 + 0.8642857145 x = -1.084233012 + 0.8642857145 Combine like terms: -1.084233012 + 0.8642857145 = -0.2199472975 x = -0.2199472975 Simplifying x = -0.2199472975Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9485187265, -0.2199472975}
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