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Simplifying 210x2 + -1680x + 1470 = 6230 Reorder the terms: 1470 + -1680x + 210x2 = 6230 Solving 1470 + -1680x + 210x2 = 6230 Solving for variable 'x'. Reorder the terms: 1470 + -6230 + -1680x + 210x2 = 6230 + -6230 Combine like terms: 1470 + -6230 = -4760 -4760 + -1680x + 210x2 = 6230 + -6230 Combine like terms: 6230 + -6230 = 0 -4760 + -1680x + 210x2 = 0 Factor out the Greatest Common Factor (GCF), '70'. 70(-68 + -24x + 3x2) = 0 Ignore the factor 70.Subproblem 1
Set the factor '(-68 + -24x + 3x2)' equal to zero and attempt to solve: Simplifying -68 + -24x + 3x2 = 0 Solving -68 + -24x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -22.66666667 + -8x + x2 = 0 Move the constant term to the right: Add '22.66666667' to each side of the equation. -22.66666667 + -8x + 22.66666667 + x2 = 0 + 22.66666667 Reorder the terms: -22.66666667 + 22.66666667 + -8x + x2 = 0 + 22.66666667 Combine like terms: -22.66666667 + 22.66666667 = 0.00000000 0.00000000 + -8x + x2 = 0 + 22.66666667 -8x + x2 = 0 + 22.66666667 Combine like terms: 0 + 22.66666667 = 22.66666667 -8x + x2 = 22.66666667 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 22.66666667 + 16 Reorder the terms: 16 + -8x + x2 = 22.66666667 + 16 Combine like terms: 22.66666667 + 16 = 38.66666667 16 + -8x + x2 = 38.66666667 Factor a perfect square on the left side: (x + -4)(x + -4) = 38.66666667 Calculate the square root of the right side: 6.218252702 Break this problem into two subproblems by setting (x + -4) equal to 6.218252702 and -6.218252702.Subproblem 1
x + -4 = 6.218252702 Simplifying x + -4 = 6.218252702 Reorder the terms: -4 + x = 6.218252702 Solving -4 + x = 6.218252702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 6.218252702 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.218252702 + 4 x = 6.218252702 + 4 Combine like terms: 6.218252702 + 4 = 10.218252702 x = 10.218252702 Simplifying x = 10.218252702Subproblem 2
x + -4 = -6.218252702 Simplifying x + -4 = -6.218252702 Reorder the terms: -4 + x = -6.218252702 Solving -4 + x = -6.218252702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -6.218252702 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.218252702 + 4 x = -6.218252702 + 4 Combine like terms: -6.218252702 + 4 = -2.218252702 x = -2.218252702 Simplifying x = -2.218252702Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.218252702, -2.218252702}Solution
x = {10.218252702, -2.218252702}
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