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Simplifying 30x2 + -235x = 175 + 0 Reorder the terms: -235x + 30x2 = 175 + 0 Combine like terms: 175 + 0 = 175 -235x + 30x2 = 175 Solving -235x + 30x2 = 175 Solving for variable 'x'. Reorder the terms: -175 + -235x + 30x2 = 175 + -175 Combine like terms: 175 + -175 = 0 -175 + -235x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-35 + -47x + 6x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-35 + -47x + 6x2)' equal to zero and attempt to solve: Simplifying -35 + -47x + 6x2 = 0 Solving -35 + -47x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5.833333333 + -7.833333333x + x2 = 0 Move the constant term to the right: Add '5.833333333' to each side of the equation. -5.833333333 + -7.833333333x + 5.833333333 + x2 = 0 + 5.833333333 Reorder the terms: -5.833333333 + 5.833333333 + -7.833333333x + x2 = 0 + 5.833333333 Combine like terms: -5.833333333 + 5.833333333 = 0.000000000 0.000000000 + -7.833333333x + x2 = 0 + 5.833333333 -7.833333333x + x2 = 0 + 5.833333333 Combine like terms: 0 + 5.833333333 = 5.833333333 -7.833333333x + x2 = 5.833333333 The x term is -7.833333333x. Take half its coefficient (-3.916666667). Square it (15.34027778) and add it to both sides. Add '15.34027778' to each side of the equation. -7.833333333x + 15.34027778 + x2 = 5.833333333 + 15.34027778 Reorder the terms: 15.34027778 + -7.833333333x + x2 = 5.833333333 + 15.34027778 Combine like terms: 5.833333333 + 15.34027778 = 21.173611113 15.34027778 + -7.833333333x + x2 = 21.173611113 Factor a perfect square on the left side: (x + -3.916666667)(x + -3.916666667) = 21.173611113 Calculate the square root of the right side: 4.601479231 Break this problem into two subproblems by setting (x + -3.916666667) equal to 4.601479231 and -4.601479231.Subproblem 1
x + -3.916666667 = 4.601479231 Simplifying x + -3.916666667 = 4.601479231 Reorder the terms: -3.916666667 + x = 4.601479231 Solving -3.916666667 + x = 4.601479231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.916666667' to each side of the equation. -3.916666667 + 3.916666667 + x = 4.601479231 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + x = 4.601479231 + 3.916666667 x = 4.601479231 + 3.916666667 Combine like terms: 4.601479231 + 3.916666667 = 8.518145898 x = 8.518145898 Simplifying x = 8.518145898Subproblem 2
x + -3.916666667 = -4.601479231 Simplifying x + -3.916666667 = -4.601479231 Reorder the terms: -3.916666667 + x = -4.601479231 Solving -3.916666667 + x = -4.601479231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.916666667' to each side of the equation. -3.916666667 + 3.916666667 + x = -4.601479231 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + x = -4.601479231 + 3.916666667 x = -4.601479231 + 3.916666667 Combine like terms: -4.601479231 + 3.916666667 = -0.684812564 x = -0.684812564 Simplifying x = -0.684812564Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.518145898, -0.684812564}Solution
x = {8.518145898, -0.684812564}
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