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Simplifying 6x2 + -21x + -70 = 0 Reorder the terms: -70 + -21x + 6x2 = 0 Solving -70 + -21x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -11.66666667 + -3.5x + x2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + -3.5x + 11.66666667 + x2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + -3.5x + x2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + -3.5x + x2 = 0 + 11.66666667 -3.5x + x2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 -3.5x + x2 = 11.66666667 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 11.66666667 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 11.66666667 + 3.0625 Combine like terms: 11.66666667 + 3.0625 = 14.72916667 3.0625 + -3.5x + x2 = 14.72916667 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 14.72916667 Calculate the square root of the right side: 3.837859647 Break this problem into two subproblems by setting (x + -1.75) equal to 3.837859647 and -3.837859647.Subproblem 1
x + -1.75 = 3.837859647 Simplifying x + -1.75 = 3.837859647 Reorder the terms: -1.75 + x = 3.837859647 Solving -1.75 + x = 3.837859647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.837859647 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.837859647 + 1.75 x = 3.837859647 + 1.75 Combine like terms: 3.837859647 + 1.75 = 5.587859647 x = 5.587859647 Simplifying x = 5.587859647Subproblem 2
x + -1.75 = -3.837859647 Simplifying x + -1.75 = -3.837859647 Reorder the terms: -1.75 + x = -3.837859647 Solving -1.75 + x = -3.837859647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.837859647 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.837859647 + 1.75 x = -3.837859647 + 1.75 Combine like terms: -3.837859647 + 1.75 = -2.087859647 x = -2.087859647 Simplifying x = -2.087859647Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.587859647, -2.087859647}
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