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Simplifying -12x2 + 70x + -28 = 0 Reorder the terms: -28 + 70x + -12x2 = 0 Solving -28 + 70x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + 35x + -6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + 35x + -6x2)' equal to zero and attempt to solve: Simplifying -14 + 35x + -6x2 = 0 Solving -14 + 35x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 2.333333333 + -5.833333333x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -5.833333333x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -5.833333333x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -5.833333333x + x2 = 0 + -2.333333333 -5.833333333x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -5.833333333x + x2 = -2.333333333 The x term is -5.833333333x. Take half its coefficient (-2.916666667). Square it (8.506944446) and add it to both sides. Add '8.506944446' to each side of the equation. -5.833333333x + 8.506944446 + x2 = -2.333333333 + 8.506944446 Reorder the terms: 8.506944446 + -5.833333333x + x2 = -2.333333333 + 8.506944446 Combine like terms: -2.333333333 + 8.506944446 = 6.173611113 8.506944446 + -5.833333333x + x2 = 6.173611113 Factor a perfect square on the left side: (x + -2.916666667)(x + -2.916666667) = 6.173611113 Calculate the square root of the right side: 2.484675253 Break this problem into two subproblems by setting (x + -2.916666667) equal to 2.484675253 and -2.484675253.Subproblem 1
x + -2.916666667 = 2.484675253 Simplifying x + -2.916666667 = 2.484675253 Reorder the terms: -2.916666667 + x = 2.484675253 Solving -2.916666667 + x = 2.484675253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = 2.484675253 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = 2.484675253 + 2.916666667 x = 2.484675253 + 2.916666667 Combine like terms: 2.484675253 + 2.916666667 = 5.40134192 x = 5.40134192 Simplifying x = 5.40134192Subproblem 2
x + -2.916666667 = -2.484675253 Simplifying x + -2.916666667 = -2.484675253 Reorder the terms: -2.916666667 + x = -2.484675253 Solving -2.916666667 + x = -2.484675253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = -2.484675253 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = -2.484675253 + 2.916666667 x = -2.484675253 + 2.916666667 Combine like terms: -2.484675253 + 2.916666667 = 0.431991414 x = 0.431991414 Simplifying x = 0.431991414Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.40134192, 0.431991414}Solution
x = {5.40134192, 0.431991414}
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