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Simplifying 6x2 + -13x2 + -4x + 4 = 0 Reorder the terms: 4 + -4x + 6x2 + -13x2 = 0 Combine like terms: 6x2 + -13x2 = -7x2 4 + -4x + -7x2 = 0 Solving 4 + -4x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.5714285714 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 0.5714285714x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 0.5714285714x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + 0.5714285714 0.5714285714x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 0.5714285714x + x2 = 0.5714285714 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 0.5714285714 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 0.5714285714 + 0.08163265305 Combine like terms: 0.5714285714 + 0.08163265305 = 0.65306122445 0.08163265305 + 0.5714285714x + x2 = 0.65306122445 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.65306122445 Calculate the square root of the right side: 0.808122036 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.808122036 and -0.808122036.Subproblem 1
x + 0.2857142857 = 0.808122036 Simplifying x + 0.2857142857 = 0.808122036 Reorder the terms: 0.2857142857 + x = 0.808122036 Solving 0.2857142857 + x = 0.808122036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 0.808122036 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.808122036 + -0.2857142857 x = 0.808122036 + -0.2857142857 Combine like terms: 0.808122036 + -0.2857142857 = 0.5224077503 x = 0.5224077503 Simplifying x = 0.5224077503Subproblem 2
x + 0.2857142857 = -0.808122036 Simplifying x + 0.2857142857 = -0.808122036 Reorder the terms: 0.2857142857 + x = -0.808122036 Solving 0.2857142857 + x = -0.808122036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -0.808122036 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.808122036 + -0.2857142857 x = -0.808122036 + -0.2857142857 Combine like terms: -0.808122036 + -0.2857142857 = -1.0938363217 x = -1.0938363217 Simplifying x = -1.0938363217Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5224077503, -1.0938363217}
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